Question

find the square root of the expression 4x^2/y^2+20x/y+13-30y/x+9^2/x^2​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{\dfrac{4x^2}{y^2}+\dfrac{20x}{y}+13-\dfrac{30y}{x}+\dfrac{9y^2}{x^2}}$

$\underline{\textsf{To find:}}$

$\textsf{The square root of}$

$\mathsf{\dfrac{4x^2}{y^2}+\dfrac{20x}{y}+13-\dfrac{30y}{x}+\dfrac{9y^2}{x^2}}$

$\underline{\textsf{Solution:}}$

$\textsf{First we write the given expression as a perfect squre}$

$\mathsf{Consider,}$

$\mathsf{\dfrac{4x^2}{y^2}+\dfrac{20x}{y}+13-\dfrac{30y}{x}+\dfrac{9y^2}{x^2}}$

$\mathsf{This\,can\,be\,written\,as}$

$\mathsf{\dfrac{4x^2}{y^2}+\dfrac{20x}{y}+13-\dfrac{30y}{x}+\dfrac{9y^2}{x^2}=\left(\dfrac{2x}{y}+p-\dfrac{3y}{x}\right)^2}$

$\mathsf{\dfrac{4x^2}{y^2}+\dfrac{20x}{y}+13-\dfrac{30y}{x}+\dfrac{9y^2}{x^2}=\left(\dfrac{2x}{y}+p-\dfrac{3y}{x}\right)\left(\dfrac{2x}{y}+p-\dfrac{3y}{x}\right)}$

$\mathsf{Equating\;coefficient\;of\;\dfrac{x}{y}\;on\;bothsides\;we\;get}$

$\mathsf{20=2p+2p}$

$\mathsf{4p=20}$

$\mathsf{p=5}$

$\implies\mathsf{\dfrac{4x^2}{y^2}+\dfrac{20x}{y}+13-\dfrac{30y}{x}+\dfrac{9y^2}{x^2}=\left(\dfrac{2x}{y}+5-\dfrac{3y}{x}\right)^2}$

$\therefore\sqrt{\mathsf{\dfrac{4x^2}{y^2}+\dfrac{20x}{y}+13-\dfrac{30y}{x}+\dfrac{9y^2}{x^2}}}\mathsf{=\pm\left(\dfrac{2x}{y}+5-\dfrac{3y}{x}\right)}$

$\underline{\textsf{Find more:}}$

Square root of polynomial m^4+6m^3+11m^2+6m+1

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