$Given\ that\ 25{{x}^{2}}-2xy+4{{y}^{2}}=0.$

$Find\ the\ value\ of\ \frac{{3x}}{{4y}}$

$25{{x}^{2}}-2xy+4{{y}^{2}}=0$

Factorize the algebraic expression using either the cross method  or special algebraic product a2-2ab+b2 = (a-b)2.

${{(5x-2y)}^{2}}=0$

Square root both sides of the equation.

$5x-2y=0$

Manipulate the equation until the left side is left with x/y.

$5x=2y$

$\frac{x}{y}=\frac{2}{5}$

Multiply both sides of the equation by 3/4.

$\frac{3}{4}\times \frac{x}{y}=\frac{3}{4}\times \frac{2}{5}$

$\frac{x}{y}=\frac{3}{{10}}$

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