Question

Show that if $a+b$ is non-zero, then the equation $a(x-a)=2ab-b(x-b)$ has a solution $x=a+b$.

Answer 1

Consider the given equation

$a(x-a)=2ab-b(x-b)$

$\Rightarrow ax-a^2=2ab-b(x-b)$

$\Rightarrow ax+bx=a^2+2ab+b^2$

$\Rightarrow (a+b)x=(a+b{)}^2$

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

$\Rightarrow x=(a+b)$ $[\because (a+b)\ne 0]$