Question

If $x^2+y^2=25$ and $xy=12$, then the value of $x^{-1}+y^{-1}$ is

• A. $\frac{12}{5}$
• B. $\frac{7}{12}$
• C. $\frac{-7}{12}$
• D. Both (B) and (C)

Answer 1

The correct option is D Both (B) and (C)

Given,

$x^2+y^2=25$

$xy=12$

We, know

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

$=25+2\times 12$

$=49$

$\therefore x+y=\pm 7$

Now, $x^{-1}+y^{-1}$ $=\frac{1}{x}+\frac{1}{y}$

$=\frac{x+y}{xy}$

$=\frac{7}{12}$ or, $\frac{-7}{12}$