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

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Solution

$| x^{2} - 5 x + 6 | + | x^{2} - 8 x + 12 | = 0$
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.
$∴ x^{2} - 5 x + 6 = 0 \Rightarrow (x - 2) (x - 3) = 0 \Rightarrow x = 2, 3$
and $x^{2} - 8 x + 12 = 0$
$\Rightarrow (x - 2) (x - 6) = 0 \Rightarrow x = 2, 6$

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

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