Question

If $(2x+3{)}^2+(2x-3{)}^2=(8x+6)(x-1)+22$, then the value of '$x$'

• A. 4
• B. 5
• C. - 1
• D. 3

Answer 1

The correct option is C - 1

We have,
$(2x+3{)}^2+(2x-3{)}^2=(8x+6)(x-1)+22$
$[\because (a+b{)}^2+(a-b{)}^2=2(a^2+b^2\left)\right]$
$\Rightarrow 2\left\{\right(2x{)}^2+3^2\}=x(8x+6)-(8x+6)+22$
$\Rightarrow 2(4x^2+9)=8x^2+6x-8x-6+22$
$\Rightarrow 8x^2+18=8x^2-2x+16$
$\Rightarrow 8x^2-8x^2+2x=16-18$
$\Rightarrow 2x=-2$
$\Rightarrow x=-1$

Hence, $x=-1$ is the solution of the given equation.