Question

The real value of $x,$ which satisfies the equation $|x^2-5x+6|+|x^2-8x+12|=0,$ is

Answer 1

$|x^2-5x+6|+|x^2-8x+12|=0$
Every modulus is a non negative number and if two non negative numbers add up to get zero, then individual numbers itself equal to zero simultaneously.
$\therefore x^2-5x+6=0\Rightarrow (x-2)(x-3)=0\Rightarrow x=2,3$
and $x^2-8x+12=0$
$\Rightarrow (x-2)(x-6)=0\Rightarrow x=2,6$

Both the equations are zero at $x=2$
Hence, $x=2$ is the only solution for the equation.