You're awesome, professor! Always explaining step by step of the resolution in a very calm way. That's the best way to teach math! Thanks from Brazil 🇧🇷
Nice question. I did it a different way: x^2=3+sqrt(8), 1/x^2=(3-sqrt(8))/(3^2-8)=3-sqrt(8), x^2+1/x^2=6. (x+1/x)^2=x^2+2+1/x^2=8, x+1/x=2*sqrt(2). x^3+1/x^3=(x+1/x)*(x^2-1+1/x^2)=2*sqrt(2)*5=10*sqrt(2).
Before watching: x^2=3+2 sqrt(2), which leads to x^2 = 1+2 sqrt(2) + 2 or (1+sqrt(2))^2. (The „old Cambridge trick“) Thus x=(1+sqrt(2)). From there I got lost in the calculation, which is why I watch the video now. 😀 I at least made it to step 1 of 4! Calculating 1/x was a clever move and remembering the (a+b)^3 formula would have helped as well!
A slightly different presentation shows the method, not just a trick that works. The intention is to find a perfect root that equals 3+2√2 with the form a^2+b^2+2ab. Or with roots A+B+2√AB. This means you need to find A+B=3 with AB=2. Just like factoring a quadratic you can solve A(3-A)=2, so A^2-3A+2=0. Or just try the factors of 2 (just 1 and 2 in this case). Similarly for 1/(√2+1) it's maybe handy to state the intention: removing the root in de numerator. Using (a+b)(a-b)=(a^2-b^2), the trick is to multiply by (a-b)/(a-b). Finally for most viewers you could skip a view steps, like √8 = 2√2.
I was able to get to x+1/x= 2x root 2. I need more practice with cube expansion. Your step when you often say " we move this to the other side" is better said by stating that you subtract the same quantity from each side of the equation or multiply both sides by (-1). In one step you go from (a+b)^3 = to (a^3+b^3)without showing how the 3ab(a+b) becomes -3ab(a+b). I enjoy your step by step explanations which are easy to follow because you label each step and each new equation.
@@christopherellis2663 Do you feel better when you are able to change a clarification of an algebra step to include a conclusion that all Americans are confused by mental arithmetic and extend your criticism further to what the observer might have eaten to not be as intelligent as you? Both statements lack proof and therefore can be considered opinions and not facts.
x=sqrt(3+sqrt(8))=sqrt((1+sqrt(2))^2)=1+sqrt(2). Since x^2=3+2*sqrt(2) and multiplying x*x^2 we get 7+5*sqrt(2). Then we add this to its inverse and using the properties of conjugate roots we obtain 7+5*sqrt(2)-7+5*sqrt(2) which equals to 10*sqrt(2).
Got the same answer by writing x^3+ 1/x^3 as(x+1/x)(x^2-1+1/x^2 etc. I ended up with 10(2+sqroot2)/ sqroot(3+2sqroot2).The denominator turned out to a perfect square= (Sqroot2+1)^2 so that gave me10(2+sqroot2)/(sqroot2)+1.After rationalising the denominator it ended up as 10 mult. by sqroot2.
l am the first person saw in this math please only l wanna 💚💜 this 🤣😂😂
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You are awesome Osman😀
Nice that you do many variants of this problem! It's gotten to the point I can go from beginning to end without consulting the video for hints. Thx!!
Sir, I marvel at your thoroughness and patient, thoughtful approach. Your explanations are very clear. Thank you! You set a good example.
You're awesome, professor! Always explaining step by step of the resolution in a very calm way. That's the best way to teach math! Thanks from Brazil 🇧🇷
You are very welcome.
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You are awesome 😀
Love and prayers from the USA!
فكرة جميلة و رائعة في حل المسألة، لا تخطر على بال احد ألا الأذكياء!!!👍👍👍
شكرا جزيلا لك...
I am from Iraq.
love this radical and cubes question, fully understand your detailed explanations in solving this Cambridge interview question
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You are awesome 😀
Nice question. I did it a different way: x^2=3+sqrt(8), 1/x^2=(3-sqrt(8))/(3^2-8)=3-sqrt(8), x^2+1/x^2=6. (x+1/x)^2=x^2+2+1/x^2=8, x+1/x=2*sqrt(2). x^3+1/x^3=(x+1/x)*(x^2-1+1/x^2)=2*sqrt(2)*5=10*sqrt(2).
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You are awesome 😀
All the methods you used are the easiest
Thank you
Very nice problem and elegant solution.
Simple but more interesting.
Thanks my dear sir.
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You are awesome Govinda 😀
Love and prayers from the USA!
Before watching: x^2=3+2 sqrt(2), which leads to x^2 = 1+2 sqrt(2) + 2 or (1+sqrt(2))^2. (The „old Cambridge trick“) Thus x=(1+sqrt(2)). From there I got lost in the calculation, which is why I watch the video now.
😀 I at least made it to step 1 of 4! Calculating 1/x was a clever move and remembering the (a+b)^3 formula would have helped as well!
Excellent!
Thank you for your feedback! Cheers!
You are awesome Philip 😀
This proves that how much command should be there in the basics, I lack basics
A slightly different presentation shows the method, not just a trick that works. The intention is to find a perfect root that equals 3+2√2 with the form a^2+b^2+2ab. Or with roots A+B+2√AB. This means you need to find A+B=3 with AB=2. Just like factoring a quadratic you can solve A(3-A)=2, so A^2-3A+2=0. Or just try the factors of 2 (just 1 and 2 in this case).
Similarly for 1/(√2+1) it's maybe handy to state the intention: removing the root in de numerator.
Using (a+b)(a-b)=(a^2-b^2), the trick is to multiply by (a-b)/(a-b).
Finally for most viewers you could skip a view steps, like √8 = 2√2.
I was able to get to x+1/x= 2x root 2. I need more practice with cube expansion. Your step when you often say " we move this to the other side" is better said by stating that you subtract the same quantity from each side of the equation or multiply both sides by (-1). In one step you go from (a+b)^3 = to (a^3+b^3)without showing how the 3ab(a+b) becomes -3ab(a+b). I enjoy your step by step explanations which are easy to follow because you label each step and each new equation.
This is how Americans are taught, because mental arithmetic is confusing for their fructose gummed brains
@@christopherellis2663 Do you feel better when you are able to change a clarification of an algebra step to include a conclusion that all Americans are confused by mental arithmetic and extend your criticism further to what the observer might have eaten to not be as intelligent as you? Both statements lack proof and therefore can be considered opinions and not facts.
The trick is sqrt(3 + sqrt(8)) => sqrt(1 + 2*sqrt(2) + 2) => sqrt( (1 + sqrt(2))^2 ) => 1 + sqrt(2)
x = 1 + sqrt(2)
x^3 = 7 + sqrt(5)
x^3 + 1/x^3 = ( (7 +sqrt(5))^2 + 1 ) / ( 7 +sqrt(5) )
solving x = 10*sqrt(2)
But your way is much better!
Thank you Sir.
x=sqrt(3+sqrt(8))=sqrt((1+sqrt(2))^2)=1+sqrt(2). Since x^2=3+2*sqrt(2) and multiplying x*x^2 we get 7+5*sqrt(2). Then we add this to its inverse and using the properties of conjugate roots we obtain 7+5*sqrt(2)-7+5*sqrt(2) which equals to 10*sqrt(2).
Nice,if i could have a teacher in my educational life.
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You are awesome Sanjoy 😀
The first step is great.
Excellent!
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You are awesome 😀
Extremely beautiful dear sir ❤️🙏🙏🙏🙏 interesting 🤔🤔🤔🤔🤔
So nice of you.
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You are awesome Z 😀
Wow, brilliant!
Thank you for such a nice video. I like it.
You are very welcome.
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You are awesome Furzaan 😀
Magnificent Sir
Excellent 👍 working
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You are awesome Ramani 😀
Got the same answer by writing x^3+ 1/x^3 as(x+1/x)(x^2-1+1/x^2 etc. I ended up with 10(2+sqroot2)/ sqroot(3+2sqroot2).The denominator turned out to a perfect square= (Sqroot2+1)^2 so that gave me10(2+sqroot2)/(sqroot2)+1.After rationalising the denominator it ended up as 10 mult. by sqroot2.
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You are awesome John 😀
Sir extremely easy question 🙏
Good
nice solution
Great. Thank you.
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You are awesome Luis 😀
Dear Sir, why have you not considered -10(sqrt(2)) also as the solution ?
Thank you🌹🌹🌹🙏
You are so welcome!
Love and prayers from the USA!
Sir, You are the Bobby Fischer of Math, No joke!
Nice, you are awesome
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You are awesome 😀
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You are the best
Incredible problem
So nice of you.
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You are awesome Julien 😀
Thank you for the video
Good ❤❤❤❤
So nice of you.
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You are awesome Vaghela 😀
very interesting question
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You are awesome Nico 😀
good qns i didnt manage to solve. but saw a pattern which i will remember.
No worries.
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You are awesome Garrick 😀
Can you explain why you chose to use the cubic formula when you could have just observed that 1/(x^3) = (1/x)^3?
Dear Stephens, 1/(x^3) = 1^3/x^3 = (1/x)^3 simple rules of exponents. Hope I explained well. Thanks for asking.
You are awesome 😀
Nice video
So nice of you.
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You are awesome 😀
Nice video🙏
Thank you
You are very welcome Rod.
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You are awesome 😀
Thnx a lot
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You are awesome Pranav 😀
Why should( a - b)*3 used instead of (a+b)*3
x^3=(1+_/2)^3=7+5_/2 after solving 5_/2+7+5_/2-7=10_/2
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You are awesome 😀
Soooooo cool.
Excellent!
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You are awesome 😀
👍👍👍👍👍👍👍👍👍👍👍👍👍👍
Thank =شكرا
Sir how are you?
I'm fine Anowar dear. Thanks for asking.
You are awesome 😀
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10√2
Easy one
🌹🌹
Excellent Engineer!
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You are awesome 😀
Bear with me. I tried doing this all in my head and came up with 13.824+(1/13.824). I'm gonna approximate and say 13.9 FINAL ANSWER!!
...and I got it wrong, folks...but pretty close for doing it all in my head!
7x=(2)^0.5 +1ans
now it's easy
x=1+2^1/2
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You are awesome Amitava 😀
oh please, why it is cambridge inverview quesion?
sqrt(3+sqrt(8)) * sqrt(3-sqrt(8)) = sqrt(9-8)= 1 solves it. It is the task for infants!
I did the question and I got 5*sqrt(8) and I was thinking where did I go wrong. Then I realised that sqrt(8) is just 2*sqrt(2). Silly me.
Ssc aspirants can do it easily 🇮🇳
Play with 2x speed
Damn that question came in my exam(9 class)
use (x+(1/x)^3)=x^3+3x+3/x+1/x^3
好
There's a way simpler than yours
Ans : 10_/2 *(Solved mentally in seconds)
10√2
@@kiranbarnwal8503 Yes you are right!!
Super!
WRONG !!!! Your way is much too long!!
Look at mindyourbrain where I solved it rapidly in 4 lines with a methodology and not with tricks!!