The solution(s) of the equation (3|x|−3)2=|x|+7 which belong to the domain of √x(x−3) is/are
A
2
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B
−2
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C
19
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D
−19
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Solution
The correct option is D−19 √x(x−3)
For the square root to be defined, x(x−3)≥0⇒x∈(−∞,0]∪[3,∞)⋯(1)
Now, given quadratic equation (3|x|−3)2=|x|+7⇒9(|x|2−2|x|+1)=|x|+7⇒9|x|2−19|x|+2=0⇒(|x|−2)(9|x|−1)=0⇒|x|=2,19⇒x=±2,±19
From equation (1), x=−2,−19