Question

x+y =12 and xy=32 find the value of x2+y2

Answer 1

Hey there !!!!

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   x+y=12 ------Equation 1

Squaring equation 1 on both sides 


  (x+y)² = 12²-----Equation 2

(a+b)²=a²+2ab+b²

Now comparing (x+y)² with (a+b)² here a=x and b=y 


So Equation 2 becomes 

  (x+y)² = 12²

  x²+2xy+y² =12²


  x²+y² = 144 - 2xy----Equation 3

But in question its given that xy= 32 

So, substituting xy = 32 in equation 3

   x²+y² =144-2*32

  x²+y² =144-64 = 80.

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Hope this helped you........................

Answer 2

x+y = 12. ---(1)
xy= 32
Squaring eq 1 both side we get
(x+y)^2 = 12^2
x^2 + y^2 + 2xy = 144. ---(2)

Putting the value of xy in eq 2
x^2 + y^2+2×32 = 144
x^2 + y^2 = 144-64
x^2 + y^2 = 80

I think it is helpful for u
Gd luck.. ☺