Question

if x+y=12 and xy=32, find the value of x^2 +y^2

Answer 1

x + y = 12 



Square on both sides,


(x + y)^2  = 12^2 

x^2 + y^2 + 2xy = 144 

x^2 + y^2 + 2(32) = 144 

x^2 + y^2  + 64 = 144 

x^2 + y^2 = 144 - 64 

x^2 + y^2  = 80 

Answer 2

Hello friends!!

Here is your answer :

x + y = 12

Squaring both sides,

${(x + y)}^{2} = {(12)}^{2}$


Using identity :

( a + b)² = a² + b² + 2ab


${(x)}^{2} + {(y)}^{2} + 2(x)(y) = 144$


${x}^{2} + {y}^{2} + 2xy = 144$

Putting the value of xy = 32


${x}^{2} + {y}^{2} + 2(32) = 144$


${x}^{2} + {y}^{2} + 64 = 144$


${x}^{2} + {y}^{2} = 144 - 64$



${x}^{2} + {y}^{2} = 80$


Hope it helps you.. ^_^

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