Question

If $x^2+y^2=25,xy=12$, then $x=$

• A. $\{3,4\}$
• B. $\{3,-3\}$
• C. $\{3,4,-3,-4\}$
• D. $\{-3,-3\}$

Answer 1

Answer: (C)

$x^2+y^2=25$ and $xy=12$
$\Rightarrow x^2+{\left(\frac{12}{x}\right)}^2=25$
$\Rightarrow x^4+144-25x^2=0$
$\Rightarrow \left(x^2-16\right)\left(x^2-9\right)=0$
$\Rightarrow x^2=16$ and $x^2=9$
$\Rightarrow x=\pm 4$ and $x=\pm 3$