Question

Given : $x:(m^2-2n)=y:(m^2+2n)$.If $3m=5x=y=15$,then the value of $n=8\frac{1}{x}$.Find the value of $x$.

Answer 1

Given, $\frac{x}{m^2-2n}=\frac{y}{m^2+2n}$
$x(m^2+2n)=y(m^2-2n)$
$x{m}^2+2xn=m^2-2yn$
$2xn+2yn=m^{2}y-m^{2}x$
$n(2x+2y)=m^2(y-x)$
$\therefore n=\frac{m^2(y-x)}{2x+2y}$
Also given, $3m=15$ then $m=5,5x=15$ then $x=3$ and $y=15$

Then $n=\frac{5^2(15-3)}{2\times 3+2\times 15}$

$\therefore n=\frac{300}{36}=8\frac{1}{3}$

$\therefore x=3$