Question

If xy = b and 1/x^2 + 1/y^2 = a, then (x + y)^2 equals =

Answer 1

Answer:

Given

$\sf \: xy = b$

$\sf \: \frac{1}{ {x}^{2} } + \frac{1 }{ {y}^{2} } = a$

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

$\sf \: {x}^{2} + {y}^{2} = a {x}^{2} {y}^{2}$

$\sf \: {x}^{2} + {y}^{2} = a {(xy)}^{2}$

$\sf \: {x}^{2} + {y}^{2} = a {b}^{2}$

Now

$\sf \: ( {x}+ {y)}^{2} = {x}^{2} +2xy + {y}^{2}$

$\sf \: ( {x}+ {y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

$\sf \: ( {x}+ {y)}^{2} = {ab}^{2} + b$

$\sf \: ( {x}+ {y)}^{2} = b ( ab + 1)$