Question

find the value x to the power of 2+ y to the power of 2,if x+y=6,xy=8​

Answer 1

Given:

If x-y=6 and xy=8, what is the value of x²+y²?

Solution:

x - y = 6, ==> x = 6 + y

x y = 8, ==> (6+y)y = 8,==> 6y + y 2  =8, ==> y 2  + 6y = 8

y 2  + 6y + 9 = 8 + 9, ==> y 2  + 6y + 9 = 17

y 2  + 6y + 9 = 17 , ==> (y + 3) 2  = 17, ==> y + 3 =  ±17−−√ , ==>

y =  ±17−−√  -3

xy = 8

x =  8y , ==>  8±17√−3 , ==>  3±17−−√  

x 2  + y 2  = ?

(3−17−−√)2+(−3−17−−√)2=52  

(3+17−−√)2+(−3+17−−√)2=52  

Answer is: 52

Answer 2

Question : Find the value of x² + y², if x + y = 6 and xy = 8

Given : x + y = 6 and xy = 8

To Find : Value of x² + y²

Answer : x² + y² = 20

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• We need to use an algebraic identify to solve this question and that identify will (a + b)² = a² + b² + 2ab

Process to Solve :

First We Take x and y in place of a and b in the algebraic identify used , Then we expand it and substitute the values which are given. Transposing the constants leave us with x² + y², and Finally we can find the value !!!

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• Take x and y in place of a and b in (a + b)² = a² + b² + 2ab

⇒ (x + y)² = x² + y² + 2xy

• Substitute the value of x + y

⇒ (6)² = x² + y² + 2xy

⇒ 36 = x² + y² + 2xy

• Substitute the Value of xy

⇒ 36 = x² + y² + 2(8)

⇒ 36 = x² + y² + 16

⇒ 36 - 16 = x² + y²

⇒ 20 = x² + y²

• Switch Sides

⇒ x² + y² = 20