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Q.
If $x ^{2}+ y ^{2}=25, xy =12$, then $x =$
Complex Numbers and Quadratic Equations
Solution:
$x^{2}+y^{2}=25$ and $x y=12$
$\Rightarrow x ^{2}+\left(\frac{12}{ x }\right)^{2}=25$
$ \Rightarrow x ^{4}+144-25 x ^{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 $x=\pm 3$