Question

if 7x+8y=2x+8y then x^2+y^2 upon x^2-y^2=?​

Answer 1

$\bold{\huge{\underline{\underline{\rm{ Given :}}}}}$

$7x + y = 2x + 8y$

$\bold{\huge{\underline{\underline{\rm{ To\:Find :}}}}}$

$\frac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } = ?$

$\rule{200}{1}$

$\green{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$7x - 2x = 8y - y$

$5x = 7y \\y = \frac{5x}{7}$

Now come to the question -

= $\frac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } \:$

Putting the value of y -

$= \frac{ {x}^{2} + ( { \frac{5x}{7}) }^{2} }{ {x}^{2} - ( { \frac{5x}{7} )}^{2} } \\ \\ = \frac{ {x}^{2} + \frac{25 {x}^{2} }{49} }{ {x}^{2} - \frac{25 {x}^{2} }{49} } \\ \\ = \frac{ \frac{49 {x}^{2} + 25 {x}^{2} }{49} }{ \frac{49 {x}^{2} - 25 {x}^{2} }{49} } \\ \\ = \frac{74 {x}^{2} }{49} \times \frac{49}{24 {x}^{2} } \\ \\ = \frac{74 {x}^{2} }{24 {x}^{2} } \\ \\ = \frac{74}{24}$

$\boxed{\red{\frac{ {x}^{2} + {y}^{2} }{ {x}^{2} - {y}^{2} } \: = \frac{37}{12} }}$

$\rule{200}{1}$

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