Question

X to the power 2 minus y to the power 2 is equal to minus 7 and x to the power 2 plus y to the power 2 is equal to 25 .find x and y.

Answer 1

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Answer 2

$Given \: x^{2} - y^{2} = 7 \: --(1)$

$and \:x^{2} + y^{2} = 25\: --(2)$

/* Add equation (1) and (2) , we get */

$\implies x^{2} - y^{2} + x^{2} + y^{2} = 7+25$

$\implies 2x^{2} = 32$

$\implies x^{2} = \frac{32}{2}$

$\implies x^{2} = 16$

$\implies x = \pm \sqrt{4^{2}}$

$\implies x = \pm 4 \: --(3)$

/* Now , subtract equation (1) from (2) , we get */

$\implies x^{2} + y^{2} -( x^{2} - y^{2} = 25 - 7$

$\implies x^{2} + y^{2} - x^{2} + y^{2} = 25 - 7$

$\implies 2y^{2} = 18$

$\implies y^{2} = \frac{18}{2}$

$\implies y^{2} = 9$

$\implies y = \pm \sqrt{3^{2}}$

$\implies y = \pm 3 \: --(4)$

Therefore.,

$\green { x = \pm 4 }$

$and \: \green { y = \pm 3 }$

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