Solve the following quadratic equation by factorization:
$\frac{1}{2a+b+2x}=\frac{1}{2a}+\frac{1}{b}+\frac{1}{2x}$

Given:

Given quadratic equation is $\frac{1}{2a+b+2x}=\frac{1}{2a}+\frac{1}{b}+\frac{1}{2x}$.

To do:

We have to solve the given quadratic equation.

Solution:

$\frac{1}{2a+b+2x}=\frac{1}{2a}+\frac{1}{b}+\frac{1}{2x}$

$\frac{1}{2a+b+2x}=\frac{(b)(2x)+(2a)(2x)+(2a)(b)}{(2a)(b)(2x)}$

$\frac{1}{2a+b+2x}=\frac{2bx+4ax+2ab}{4abx}$

$1(4abx)=(2a+b+2x)(2bx+4ax+2ab)$

$4abx=2a(2bx+4ax+2ab)+b(2bx+4ax+2ab)+2x(2bx+4ax+2ab)$

$4abx=4abx+8a^2x+4a^2b+2b^2x+4abx+2ab^2+4bx^2+8ax^2+4abx$

$(4b+8a)x^2+(8a^2+2b^2+4ab+4ab)x+4a^2b+2ab^2=0$

$2[(4a+2b)x^2+(4a^2+b^2+4ab)x+2a^2b+ab^2]=0$

$2(2a+b)x^2+(2a+b)^2x+ab(2a+b)=0$

$(2a+b)[2x^2+(2a+b)x+ab]=0$

$2x^2+2ax+bx+ab=0$

$2x(x+a)+b(x+a)=0$

$(2x+b)(x+a)=0$

$2x+b=0$ or $x+a=0$

$2x=-b$ or $x=-a$

$x=-\frac{b}{2}$ or $x=-a$

The values of $x$ are $-\frac{b}{2}$ and $-a$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

72 Views

Kickstart Your Career

Get certified by completing the course

Get Started