Question

m2 - 5 m = -3 solve with complete square method​

Answer 1

Answer:

$\sf{The \ roots \ of \ the \ given \ equation \ are}$

$\sf{\dfrac{5+\sqrt{13}}{2} \ and \ \dfrac{5-\sqrt{13}}{2}.}$

Given:

$\sf{m^{2}-5m=-3}$

To find:

$\sf{Roots \ of \ the \ equation \ by \ completing \ square \ method.}$

Solution:

$\sf{\leadsto{m^{2}-5m=-3}}$

__________________

$\sf{(\dfrac{1}{2}\times \ Coefficient \ of \ x)^{2}}$

$\sf{=[\dfrac{1}{2}\times \ (-5)]^{2}}$

$\sf{=\dfrac{25}{4}}$

__________________

$\sf{Add \ \dfrac{25}{4} \ on \ both \ the \ sides, \ we \ get}$

$\sf{\leadsto{m^{2}-5m+\dfrac{25}{4}=-3+\dfrac{25}{4}}}$

$\sf{\leadsto{(m-\dfrac{5}{2})^{2}=\dfrac{13}{4}}}$

$\sf{On \ taking \ square \ root \ of \ both \ sides}$

$\sf{\leadsto{m-\dfrac{5}{2}=\pm\dfrac{\sqrt{13}}{2}}}$

$\sf{\leadsto{m=\dfrac{5\pm\sqrt{13}}{2}}}$

$\sf\purple{\tt{\therefore{The \ roots \ of \ the \ given \ equation \ are}}}$

$\sf\purple{\tt{\dfrac{5+\sqrt{13}}{2} \ and \ \dfrac{5-\sqrt{13}}{2}.}}$