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Question

The number of value(s) of x satisfying the equation (x+9)2+8|x+9|+7=0 is

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Solution

(x+9)2+8|x+9|+7=0
|x+9|2+8|x+9|+7=0(|x2|=|x|2)

Let |x+9|=t
t2+8t+7=0
t2+7t+t+7=0
(t+7)(t+1)=0
t=7,1
We know that |x+9|0t0

Hence, no values of x is possible.

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