Question

Solve : $\frac{(5x+2{)}^2-(5x-2{)}^2}{(5x+2{)}^2+(5x-2{)}^2}=\frac{12}{13}$

Answer 1

We have,

$\frac{{(5x+2)}^2-{(5x-2)}^2}{{(5x+2)}^2+{(5x-2)}^2}=\frac{12}{13}$

$\frac{25x^2+4+20x-(25x^2+4-20x)}{25x^2+4+20x+25x^2+4-20x}=\frac{12}{13}$

$\frac{25x^2+4+20x-25x^2-4+20x}{25x^2+4+20x+25x^2+4-20x}=\frac{12}{13}$

$\frac{40x}{50x^2+8}=\frac{12}{13}$

$\frac{20x}{25x^2+4}=\frac{12}{13}$

$260x=300x^2+48$

$300x^2-260x+48=0$

$75x^2-65x+4=0$

$75x^2-60x-5x+4=0$

$15x(5x-4)-1(5x-4)=0$

$(5x-4)(15x-1)=0$

$x=\frac{1}{15},\frac{4}{5}$

Hence, this is the answer.