Question

x-y=7 xy=9 find the value of x2+y2

Answer 1

$x-y = 7\\ \\ \Rightarrow (x-y)^2 = 7^2\\ \\ \Rightarrow x^2+y^2-2xy=49 \\ \\ \Rightarrow x^2+y^2-2 \times 9=49 \\ \\ \Rightarrow x^2+y^2-18=49 \\ \\ \Rightarrow x^2+y^2= 49+18\\ \\ \Rightarrow x^2+y^2 = 67$

Answer 2

Hi there!

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Given :

x - y = 7

xy = 9

To find :

x² + y²

$\mathsf{\boxed{\bold{Solution :}}}$

$x - y = 7 \\ \\ \bold{on \: squaring \: both \: sides.}\\ \\ (x - y) {}^{2} = (7) {}^{2} \\ \\ x {}^{2} + y {}^{2} - 2xy = 49 \\ \\ x {}^{2} + y {}^{2} - 2 \times 9 = 49 \\ \\ x {}^{2} + y {}^{2} - 18 = 49 \\ \\ x {}^{2} + y {}^{2} = 49 + 18 \\ \\ \boxed { \mathsf{\red{ \bold{x {}^{2} + y {}^{2} = 67}}}}$

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Thanks for the question!

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