Question

If $15(2x^2-y^2)=7xy,$ find the ratio of x : y.

Answer 1

Given that $15(2x^2-y^2)=7xy$

$\Rightarrow 30x^2-15y^2-7xy=0$

Now divide the above equation by $y^2$ on both sides

$\Rightarrow 30(\frac{x}{y}{)}^2-7(\frac{x}{y})-15=0$

Let $\frac{x}{y}=t$, so we get quadratic equation in $t$

$\Rightarrow 30t^2-7t-15=0$

The roots of above equation are $t=\frac{7\pm \sqrt{49+1800}}{60}$

$\Rightarrow t=\frac{7\pm 43}{60}=\frac{5}{6},-\frac{3}{5}$

Therefore ratio of $x:y$ is $5:6$ or $-3:5$