Question

If $x^2+y^2=25,xy=12$, then the number of values of $x$ is

• A. $1$
• B. $2$
• C. $4$
• D. $0$

Answer 1

The correct option is C $4$

$x^2+y^2=25,xy=12$
Substitute $y=\frac{12}{x}$, we get

$\Rightarrow x^2+{\left[\frac{12}{x}\right]}^2=25\Rightarrow x^4+144-25x^2=0$

$\Rightarrow (x^2-16)(x^2-9)\Rightarrow x^2=16$ and $x^2=9$
$\Rightarrow x=\pm 4$ and $x=\pm 3$

$\therefore$ Total number of values of $x$ is $4$.

Hence, option C.