Question

If 1/x + 1/y = 1/2 & 1/x- 1/y = 1/4 , find 1/x² - 1/y² Can you find this? Challenge to you.☠️

Answer 1

Step-by-step explanation:

$\frac{1}{x} + \frac{1}{y} = \frac{1}{2}$

$\frac{2(y + x)}{xy} = 1$

$(y + x) = \frac{xy}{2}$

$\frac{1}{x} - \frac{1}{y} = \frac{1}{4}$

$\frac{4(y - x)}{xy} = 1$

$(y - x) = \frac{xy}{4}$

Solve 1 and 2

y-x = xy /4

y+x = xy /2

solve two equations

$x = \frac{3}{2}$

put x value in 1 st equation

$y = 6$

$\frac{1}{ \frac{9}{4} } - \: \frac{1}{36}$

$\frac{4}{9} - \frac{1}{36}$

$\frac{144 - 9}{324}$

$\frac{</p><p>135}{324}$

THIS IS THE ANSWER