$latex Given\ that\ 25{{x}^{2}}-20xy+4{{y}^{2}}=0.$
$latex Find\ the\ value\ of\ \frac{{3x}}{{4y}}$
$latex 25{{x}^{2}}-20xy+4{{y}^{2}}=0$
Factorize the algebraic expression using either the cross method or special algebraic product a2-2ab+b2 = (a-b)2.
$latex {{(5x-2y)}^{2}}=0$
Square root both sides of the equation.
$latex 5x-2y=0$
Manipulate the equation until the left side is left with x/y.
$latex 5x=2y$
$latex \frac{x}{y}=\frac{2}{5}$
Multiply both sides of the equation by 3/4.
$latex \frac{3}{4}\times \frac{x}{y}=\frac{3}{4}\times \frac{2}{5}$
$latex \frac{x}{y}=\frac{3}{{10}}$
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