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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