Question

Solve the following quadratic equation for X
X square - 4aX - b square + 4a square = 0

Answer 1

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

$\textsf{Quadratic equation is}$

$\mathsf{x^2-4ax-b^2+4a^2=0}$

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

$\textsf{Roots of the given quadratic equation}$

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

$\mathsf{Consider,}$

$\mathsf{x^2-4ax-b^2+4a^2=0}$

$\mathsf{(x^2-4ax+4a^2)-b^2=0}$

$\textsf{Using the identity,}\;\boxed{\mathsf{a^2-2ab+b^2=(a-b^2)}}$

$\textsf{we get}$

$\mathsf{(x-2a)^2-b^2=0}$

$\mathsf{Factorize\;using\;the\;identity}$

$\boxed{\mathsf{a^2-b^2=(a-b)(a+b)}}$

$\mathsf{(x-2a-b)(x-2a+b)=0}$

$\implies\mathsf{x-2a-b=0\;\;\&\;\;x-2a+b=0}$

$\implies\mathsf{x=2a+b\;\;\&\;\;x=2a-b}$

$\therefore\mathsf{Roots\;are\;\;2a+b\;\;and\;\;2a-b}$

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