Find roots of the given quadratic equations by using quadratic formula

1.	Find roots of the given quadratic equations by using quadratic formula 1by2 x square minus root 11x +1=0
Answer» $\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$ $\sf{Roots \ are \ \sqrt10+\sqrt11 \ and \ -\sqrt10+\sqrt11}$ $\sf\orange{Given:}$ $\sf{The \ given \ quadratic \ equation \ is}$ $\sf{\implies{\frac{1x^{2}}{2}-\sqrt11+1=0}}$ $\sf\pink{To \ find:}$ $\sf{The \ roots \ of \ the \ equation \ by}$ $\sf{completing \ the \ square \ method.}$ $\sf\green{\underline{\underline{Solution:}}}$ $\sf{The \ given \ quadratic \ equation \ is}$ $\sf{\implies{\frac{1x^{2}}{2}-\sqrt11+1=0}}$ $\sf{Multiply \ equation \ by \ 2 \ throughout}$ $\sf{\implies{x^{2}-2\sqrt11x+2=0}}$ $\sf{Here, \ Coefficient \ of \ x^{2}=1}$ $\sf{Coefficient \ of \ x=-2\sqrt11}$ $\sf{Constant=2}$ $\sf{\implies{x^{2}-2\sqrt11x+11=-1}}$ _______________________________ $\sf{\implies{(\frac{1}{2}\times \ Coefficient \ of \ x)^{2}}}$ $\sf{implies{(\frac{1}{2}\times \ -2\sqrt11)^{2}}}$ $\sf{\implies{(\frac{-2\sqrt11}{2})^{2}}}$ $\sf{\implies{(-\sqrt11)^{2}}}$ $\sf{\implies{11}}$ _______________________________ $\sf{Add \ 11 \ on \ both \ sides \ of \ equation}$ $\sf{\implies{x^{2}-2\sqrt11x+11=-1+11}}$ $\sf{\implies{x^{2}-2\sqrt11x+11=10}}$ $\sf{\implies{(x-\sqrt11)^{2}=10}}$ $\sf{On \ taking \ square \ root \ of \ both \ sides}$ $\sf{\implies{x-\sqrt11=\sqrt10 \ or \ -\sqrt10}}$ $\sf{\implies{x=\sqrt10+\sqrt11 \ or \ -\sqrt10+\sqrt11}}$ $\sf\purple{\tt{\therefore{Roots \ are \ \sqrt10+\sqrt11 \ and \ -\sqrt10+\sqrt11}}}$