Question

by factorize method​

Answer 1

Given :-

$(2x -1 ) ( x -3) = (x + 5) (x -1)$

To solve :-

By Factorization method.

Solution:-

First multiple the terms in L. H. S Or R. H. S side.

$2x (x-3) -1 (x-3) = x (x-1) +5(x-1)$

$2x^2 -6x -x +3 = x^2 -x +5x -5$

Now solve variables and constant separately.

$2x^2-x^2-6x-5x+3+5=0$

$x^2 -11x+8$

Now applying Shridicharya charya rule,

a = 1 , b = -11 c = 8

$D = b^2 - 4.a.c$

$D = (-11) ^2-4.1.8$

$D = 121 -32$

$D = 89$

Let calculate it's roots :-

$x= \dfrac{-b\pm\sqrt{D}}{2a}$

$x = \dfrac {11\pm\sqrt{89}}{2}$

$x = \dfrac {11\pm\sqrt{89}}{2}$

hence, the two values of equation are :-

$x = \dfrac {11+\sqrt{89}}{2}$

and,

$x = \dfrac {11-\sqrt{89}}{2}$