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The first step I would make is moving sqrt(2) to the right. This puts variables on one side, constants on the other. Then square both sides resulting in: sqrt(x)^2 = (2 - sqrt(2))^2. x = 2^2 - 2(2*sqrt(2)) + sqrt(2)^2. All that's left is collecting terms and simplifying.❤
I solved a little different: √2 + √x = 2 √x = 2 - √2 (√x)^2 = (2 - √2)^2 x = 4 - 4√2 + 2 x = 6 - 4√2 There are only this solution for "x" in this problem.
if the final answer is an irrational number, there is no point in doing the transformations. You can simply calculate in the first calculus by taking 2 from the radical
@@Alamaths Here's the translation: I’m learning a lot from watching your videos. I’m an ordinary working professional in my 50s living in Korea, and watching these videos brings back memories of my school days. I couldn’t leave a polite comment because I’m not very confident in English, but your videos have been a great help, and I enjoy watching them.
Sorry to bother, but this is overly complicated (and false). By squaring an equation you can create extraneous solutions (you did! x=6+4√2 is false). Much easier would be to just substract √2 from both sides and only then to square the equation. This gives directly x=6-4√2 which is the only solution. The reason behind this is the "dichotomy" of squares and roots: √4 has only one(!) solution: "2". But x²=4 has two solutions: +√4 = +1 * 2 = "2" and -√4 = -1 * 2 = "-2"
1.bərabərliyin hər iki tərəfini 2-yə bölüb qüvvətə yüksəltdikdən sonra 4-ə vurmaq nəyə lazım idi?Elə birbaşa qüvvətə yüksəltsə idiniz eyni nəticə alınacaqdı. 2. X^2-12X+4=0 şevrilmiş kvadrat tənlik olduğundan onun köklərini X=-P/2+-*(P/2)^2 -q kimi həll etsə idiniz daha əlverişli olmazdımı? Təşəkkürlər.
Siempre cuando obtengas un número al cuadrado, como lo haces, pierdes información crucial sobre el número que elevas al cuadrado. Esa información es la positividad o negatividad del número. Para ser precisos, en el momento que elevas al cuadrado a 2 - x, estás permitiendo que 2 - x sea negativo y esto no puede ser. Es por eso que obtienes dos soluciones a la ecuacion cuadrática, que no tienen por qué ser soluciones de la ecuación original. De hecho desde la ecuación original tenemos que solo habrá una solución obtenida como alguien te comentó antes. x = sqrt(2 - sqrt(2)).
Совершенно нерациональный способ решения. И результат ошибочный: два корня вместо одного. Если автор видео запутался в решении такой примитивной задачи, которая была рассмотрена, то ему должно быть очень стыдно и лучше впредь не пытаться заниматься математикой.
It takes 1 minute.Wasting 8 minutes is funny and foolishness. 2nd step..square root of x=2-root 2 Squaring both sides x=2-root2 whole square. = 4+2-4root 2. = 6-4root2. Mind that VIEWERS are not L.K.G. students. By seeing your time wasting version , I remeber one saying, Digging a MOUNTAIN and getting a RAT.😂😂😂😂😂😂😂😂😂😂😂😂😂. It clearly means that basically you do not know simple methods and time saving skills.If you have perfect and thorough knowledge, by adopting simple methods and easy tricks one fourth of time is sufficient. Or else you can as well keep HEADING ' LESSON FOR 6th CLASS KIDS"😂😂😂😂😂
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I hope you all are well 🤗🤗🤗
If you like this video about
How to solve this math problem
Please like and subscribe to my channel as it helps me a lot，🙏🙏🙏🙏
❤❤🎉🎉
√2 + √x = 2 → where: x ≥ 0
√x = 2 - √2
(√x)² = (2 - √2)²
x = 4 - 4√2 + 2
x = 6 - 4√2
Wow 😮, thank you so much for the comments 👍❤ .
Where are you watching from 💖?
@@Alamaths I'm watching from France
@@key_board_x Wow, thanks 😊
Thank you for explaining. The solution is (only) x=6-4√2 . [ x=6+4√2 must be rejected. ] Please check.
Great 👍. It is true. Thanks for the comments. Are you a maths teacher 💖?
I calculated under 15 seconds, should have done it head but not today. From Finland.
Dear teacher I solved a little different:
√2 + √x = 2
√x = 2 - √2
(√x)^2 = (2 -√2)^2
x = 4 - 4√2 + 2
x = 6 - 4√2
This is de only solution.
Thanks
@@Alamaths In the past, I was a math teacher in Japan.
@@Alamathsx = 6+4√2 >2 không thỏa mãn đầu bài. Tác giả tự làm phức tạp bài toán √2+√x=2, -> √x= 2-√2,-> x= (2-√2)(2-√2)= 4-4√2+2= 6-4√2.
x^0.5 = 2 - 2^0.5
Square both sides
x = 4 - 4.2^0.5 + 2
x = 6 - 4.2^0.5
I agree The solution is only x=6-4√2 . I had a great deal work to verify this solution in the original equation in an exactly way.
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The first step I would make is moving sqrt(2) to the right. This puts variables on one side, constants on the other. Then square both sides resulting in:
sqrt(x)^2 = (2 - sqrt(2))^2.
x = 2^2 - 2(2*sqrt(2)) + sqrt(2)^2.
All that's left is collecting terms and simplifying.❤
Yes. Thanks for the comments 👍
Where are you watching from 💖?
I solved a little different:
√2 + √x = 2
√x = 2 - √2
(√x)^2 = (2 - √2)^2
x = 4 - 4√2 + 2
x = 6 - 4√2
There are only this solution for "x" in this problem.
Yes. Thanks for the comments 👍.
Where are you watching from 💖?
@@Alamaths
I am watching from São Paulo - Brazil.🇧🇷🇧🇷
@toninhorosa4849 wow, thanks for the comments 👍. Where are you watching from 💖?
Through this math you are trying to express yourself that what a scholar
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Thanks so much sirr 😊
❤❤ thanks for the comments
sqrt(x) = 2 - sqrt(2) >> x = 0.343 (elementary school)
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Good one there! 😊
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Impressed the way you present math to beginners. Great job 👏
Speaking from India.
Wow, thank you!
Too many unnecessary steps. Sol. 6+4√2 is incorrect.
√2+√x=2
√x=2-√2
x=(2-√2)^2
x=4-2*2√2+2
x=6-4√2
Thanks for the comments 👍
Are you a maths teacher 💖?
@@Alamaths no, I am not. I am an engineer.
√x+√2=2
X=(2-√2) ^ 2= 4+2-2×2√2
=6-4√2=2(3-2√2)
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√x=2--√2>>>square both sides.etc.
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if the final answer is an irrational number, there is no point in doing the transformations. You can simply calculate in the first calculus by taking 2 from the radical
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incorect
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@@Alamaths Here's the translation:
I’m learning a lot from watching your videos. I’m an ordinary working professional in my 50s living in Korea, and watching these videos brings back memories of my school days. I couldn’t leave a polite comment because I’m not very confident in English, but your videos have been a great help, and I enjoy watching them.
@@seedseed7801 thanks 😊
Thầy hãy thử với nghiệm x1 nhé
Ok... thanks for the reply 👍. Where are you watching from 💖?
It is rather long way.
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@@Alamaths No,I am not,only a teacher
√x=2-√2 ; i,e x=4+2-4√2 ; x=6-4√2 2nd method. √2+√x=2 ; i,e 2+x+2√2x=4 ; i,e x+2√2x=2 ; 2√2x=2-x ; 8x=x^2+4-4x ; x^2-12x+4=0 ; x= (12+√144-16)/2 or x= (12-√144-16)/2 ; i,e x= (12+8√2)/2 ; x= 6+4√2 or x= 6-4√2
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Are you a professor of maths 💖?
Sorry to bother, but this is overly complicated (and false). By squaring an equation you can create extraneous solutions (you did! x=6+4√2 is false).
Much easier would be to just substract √2 from both sides and only then to square the equation. This gives directly x=6-4√2 which is the only solution.
The reason behind this is the "dichotomy" of squares and roots:
√4 has only one(!) solution: "2".
But x²=4 has two solutions: +√4 = +1 * 2 = "2" and -√4 = -1 * 2 = "-2"
Great 👍. Thanks for the comments.
Are you a professor of maths 💖?
@@Alamaths No, I am "just" an engineer.
@@1zaj34 okay 👍. Thanks for the reply.
Yes. I noticed this too. Watch out for extraneous roots. And yes, there is a much easier way to solve.
in: √(2x) = (2-x)/2
(2-x)/2 must be ⩾0
So: 2 ⩾ x
So: x ≤ 2
But: 6 + 4√2 ⩾ 2
So: 6 + 4√2 is not solution
S = { 6 - 4√2 }
Because: (6 - 4√2) ≤ 2
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@@Alamaths
From Morocco
@@mohamedkhatimi8938 Great 👍. How is everything over there?
@@Alamaths
Very nice
√x = 2 - √2. X = (2 -√2)......
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1.bərabərliyin hər iki tərəfini 2-yə bölüb qüvvətə yüksəltdikdən sonra 4-ə vurmaq nəyə lazım idi?Elə birbaşa qüvvətə yüksəltsə idiniz eyni nəticə alınacaqdı.
2. X^2-12X+4=0 şevrilmiş kvadrat tənlik olduğundan onun köklərini
X=-P/2+-*(P/2)^2 -q kimi həll etsə idiniz daha əlverişli olmazdımı?
Təşəkkürlər.
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Məlum bir tərəfə məhcul digər tərəfə etməklə alınan ifadə sqrt(x)=2-sqrt(2)
6-4 root 2 is the onlycorrect answer
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Siempre cuando obtengas un número al cuadrado, como lo haces, pierdes información crucial sobre el número que elevas al cuadrado. Esa información es la positividad o negatividad del número.
Para ser precisos, en el momento que elevas al cuadrado a 2 - x, estás permitiendo que 2 - x sea negativo y esto no puede ser.
Es por eso que obtienes dos soluciones a la ecuacion cuadrática, que no tienen por qué ser soluciones de la ecuación original. De hecho desde la ecuación original tenemos que solo habrá una solución obtenida como alguien te comentó antes.
x = sqrt(2 - sqrt(2)).
Noted. Thanks for the comments 👍
Are you a professor of maths 💖 🤔?
@@Alamaths Yes, I am
Redondeado
x = 0,343...es irracional
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Math Olympiad: √2 + √x = 2; x =?
2 > √2 > 1 > √x > 0; √x = 2 - √2, x = (√x)² = (2 - √2)² = 2² - 4√2 + (√2)² = 6 - 4√2
Answer check:
x = 6 - 4√2 = (2 - √2)²; √x = 2 - √2, √2 + √x = 2; Confirmed
Final answer:
x = 6 - 4√2
Note:
If: x = 6 + 4√2 > 9, √2 + √x > 3; x ≠ 6 + 4√2
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@@Alamaths USA
@@walterwen2975 Wow, thanks.
How is everything over there?
عندما نعوض قيمة xالناتجه في المعادله نجد ان الطرف الأيسر لا يساوي الطرف الأيمن اذن الحل خطاء
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This is easy math, not Olympiad level
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not good! at 3:00 to take square on both side, x must be >=0 and x must be
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@@Alamaths from algeria👍
@@conarddranoc7618 Great 👍. Thanks for the comments.
dekti mono 6-4.i,41....
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@@Alamaths Greece..
@@ΔΗΜΗΤΡΗΣΑΓΑΤΣΑΣ Wow, thanks 😊
+ ve never right
You can check
6+4sqrt(2)=12. ... It is not the solution!!!!
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You square both sides so you end up with
2 + x = 2^2
X = 4 - 2
X = 2
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Huh, this is a joke, right?
@@1zaj34 why
@@nufailanoon Because, if you square "√2 + √x" the anser is not(!) "2 + x" but "2 + 2√2√x + x". Binomial theorem: (a + b)^2 = a^2 + 2ab + b^2
@@1zaj34 Oh yea
(a + b) ^2 is a^2 +2ab + b^2
But I thought the square will cancel the square roots?
Laughable way of solving...its like spaghetti...simplify first by putting x on 1 side then constants on the other side...see comments above
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This is so wrong!
Too worse time
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!/x=2-!/2
X=(2-!/2)²=4-4!/2+2=6-4!/2
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@@Alamaths yes
Совершенно нерациональный способ решения. И результат ошибочный: два корня вместо одного. Если автор видео запутался в решении такой примитивной задачи, которая была рассмотрена, то ему должно быть очень стыдно и лучше впредь не пытаться заниматься математикой.
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jajajaj most of people speak English.
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Stay away from mathematics .you made it too complicated .
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√2 + √X = 2
√X = 2 - √2
(√X)^2 = (2 - √2)^2
X = (2 - √2) (2 - √2)
X = 4 - 2√2 - 2√2 + 2
X = 6 - 4√2
Let's check!!
X = 6 - 4√2 = 0.34314..
√2 + √0.34314.. = 2
FYI: For X = 6 + 4√2
X = 6 + 4√2 = 11.65685..
√2 + √11.65685.. = 4.8284..
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Ведь элементарный пример, зачем усложнять простейшее, не пойму!
It takes 1 minute.Wasting 8 minutes is funny and foolishness.
2nd step..square root of x=2-root 2
Squaring both sides
x=2-root2 whole square.
= 4+2-4root 2.
= 6-4root2.
Mind that VIEWERS are not L.K.G. students.
By seeing your time wasting version ,
I remeber one saying,
Digging a MOUNTAIN and getting a RAT.😂😂😂😂😂😂😂😂😂😂😂😂😂.
It clearly means that basically you do not know
simple methods and time saving skills.If you have perfect and thorough knowledge, by adopting
simple methods and easy
tricks one fourth of time is sufficient. Or else you can as well keep HEADING ' LESSON FOR 6th CLASS KIDS"😂😂😂😂😂
Great, Prof . Thanks for the comments 👍
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