At about 12:00 "Case 2" x² + y ² = -√(50). Surely the LHS is positive and this must be rejected, unless you are about to entertain complex solutions. Expressions like √(2 + √5) can sometimes be simplified as "a + b√5", altho I have forgotten what the limitations are. Please make a video on denesting radical expressions.
Why do you always make maths more complicated than it is. You should just solve X^2-y^2=sqrt(10) with X^2+y^2=sqrt(50) simultaneously. And get their square root after. Very silly
@@superacademy247 I did watch it. you just like to go the long way and extend the video unnecessarily and waste everyone’s time . Happy new year to you too
At about 12:00 "Case 2" x² + y ² = -√(50). Surely the LHS is positive and this must be rejected, unless you are about to entertain complex solutions. Expressions like √(2 + √5) can sometimes be simplified as "a + b√5", altho I have forgotten what the limitations are. Please make a video on denesting radical expressions.
There are many videos in my channel on denesting but I'll make more videos ✅ using different methods 🎁🎉🥳🎄
x² - y² = √10 → given: xy = √10 → x²y² = 10 → y² = 10/x²
x² - (10/x²) = √10
(x⁴ - 10)/x² = √10
x⁴ - 10 = x²√10
x⁴ - x²√10 - 10 = 0
Δ = (- √10)² - (4 * - 10) = 10 + 40 = 50 = 2 * 5²
x² = (√10 ± 5√2)/2
First case: x² = (√10 + 5√2)/2
Recall: y² = 10/x²
y² = 10/[(√10 + 5√2)/2]
y² = 20/(√10 + 5√2)
y² = 20.(√10 - 5√2)/[(√10 + 5√2).(√10 - 5√2)]
y² = 20.(√10 - 5√2)/[10 - 50]
y² = 20.(√10 - 5√2)/- 40
y² = (5√2 - √10)/2
x² + y² = [(√10 + 5√2)/2] + [(5√2 - √10)/2]
x² + y² = [(√10 + 5√2) + (5√2 - √10)]/2
x² + y² = (√10 + 5√2 + 5√2 - √10)/2
x² + y² = (10√2)/2
x² + y² = 5√2
Restart
x² - y² = √10
(x + y).(x - y) = √10
(x + y)².(x - y)² = 10
(x + y)².(x² + y² - 2xy) = 10 → recall: x² + y² = 5√2
(x + y)².(5√2 - 2xy) = 10 → given: xy = √10
(x + y)².(5√2 - 2√10) = 10
(x + y)² = 10/(5√2 - 2√10)
(x + y)² = 10.(5√2 + 2√10)/[(5√2 - 2√10).(5√2 + 2√10)]
(x + y)² = 10.(5√2 + 2√10)/[50 - 40]
(x + y)² = 5√2 + 2√10
x + y = ± √(5√2 + 2√10)
Second case: x² = (√10 - 5√2)/2 ← this is a negative number → x is a complex number
Recall: y² = 10/x²
y² = 10/[(√10 - 5√2)/2]
y² = 20/(√10 - 5√2)
y² = 20.(√10 + 5√2)/[(√10 - 5√2).(√10 + 5√2)]
y² = 20.(√10 + 5√2)/[10 - 50]
y² = 20.(√10 + 5√2)/- 40
y² = - (√10 + 5√2)/2 ← this is a negative number → y is a complex number
x² + y² = [(√10 - 5√2)/2] + [- (√10 + 5√2)/2]
x² + y² = [(√10 - 5√2) - (√10 + 5√2)]/2
x² + y² = (√10 - 5√2 - √10 - 5√2)/2
x² + y² = - (10√2)/2
x² + y² = - 5√2
Restart
x² - y² = √10
(x + y).(x - y) = √10
(x + y)².(x - y)² = 10
(x + y)².(x² + y² - 2xy) = 10 → recall: x² + y² = - 5√2
(x + y)².(- 5√2 - 2xy) = 10 → given: xy = √10
(x + y)².(- 5√2 - 2√10) = 10
(x + y)² = - 10/(5√2 + 2√10)
(x + y)² = - 10.(5√2 - 2√10)/[(5√2 + 2√10).(5√2 - 2√10)]
(x + y)² = - 10.(5√2 - 2√10)/[50 - 40]
(x + y)² = (5√2 - 2√10).i²
x + y = ± i√(5√2 - 2√10)
Summarize:
x + y = ± √(5√2 + 2√10)
x + y = ± i√(5√2 - 2√10)
Why do you always make maths more complicated than it is. You should just solve X^2-y^2=sqrt(10) with X^2+y^2=sqrt(50) simultaneously. And get their square root after. Very silly
Watch and learn 😎. Happy new year 🎉🥳🎉🎁🎄
@@superacademy247 I did watch it. you just like to go the long way and extend the video unnecessarily and waste everyone’s time . Happy new year to you too