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Question

The real value of x, which satisfies the equation |x25x+6|+|x28x+12|=0, is 


Solution

|x25x+6|+|x28x+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.
x25x+6=0(x2)(x3)=0x=2,3
and x28x+12=0
(x2)(x6)=0x=2,6

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

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