Question

Find roots of the given quadratic equations by using quadratic formula 1by2 x square minus root 11x +1=0

Answer 1

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{Roots \ are \ \sqrt10+\sqrt11 \ and \ -\sqrt10+\sqrt11}$

$\sf\orange{Given:}$

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{\implies{\frac{1x^{2}}{2}-\sqrt11+1=0}}$

$\sf\pink{To \ find:}$

$\sf{The \ roots \ of \ the \ equation \ by}$

$\sf{completing \ the \ square \ method.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{\implies{\frac{1x^{2}}{2}-\sqrt11+1=0}}$

$\sf{Multiply \ equation \ by \ 2 \ throughout}$

$\sf{\implies{x^{2}-2\sqrt11x+2=0}}$

$\sf{Here, \ Coefficient \ of \ x^{2}=1}$

$\sf{Coefficient \ of \ x=-2\sqrt11}$

$\sf{Constant=2}$

$\sf{\implies{x^{2}-2\sqrt11x+11=-1}}$

_______________________________

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

$\sf{implies{(\frac{1}{2}\times \ -2\sqrt11)^{2}}}$

$\sf{\implies{(\frac{-2\sqrt11}{2})^{2}}}$

$\sf{\implies{(-\sqrt11)^{2}}}$

$\sf{\implies{11}}$

_______________________________

$\sf{Add \ 11 \ on \ both \ sides \ of \ equation}$

$\sf{\implies{x^{2}-2\sqrt11x+11=-1+11}}$

$\sf{\implies{x^{2}-2\sqrt11x+11=10}}$

$\sf{\implies{(x-\sqrt11)^{2}=10}}$

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

$\sf{\implies{x-\sqrt11=\sqrt10 \ or \ -\sqrt10}}$

$\sf{\implies{x=\sqrt10+\sqrt11 \ or \ -\sqrt10+\sqrt11}}$

$\sf\purple{\tt{\therefore{Roots \ are \ \sqrt10+\sqrt11 \ and \ -\sqrt10+\sqrt11}}}$