JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The sum of the solutions of the equation \(\left| {\sqrt x - 2} \right| + \sqrt x \left( {\sqrt x - 4} \right) + 2 = 0\left( {x > 0} \right)\) is equal to
- A \(9\)
- B \(4\)
- C \(10\)
- D \(12\)
Answer & Solution
Correct Answer
(C) \(10\)
Step-by-step Solution
Detailed explanation
\(|\sqrt{x}-2|+\sqrt{x}(\sqrt{x}-4)+2=0\) \(|\sqrt{x}-2|+(\sqrt{x})^{2}-4 \sqrt{x}+2=0\) \(|\sqrt{x}-2|^{2}+|\sqrt{x}-2|-2=0\) \(|\sqrt{x}-2|=-2(\text { not possible })\) or \(|\sqrt{x}-2|=1\) \(\sqrt{x}-2=1,-1\) \(\sqrt{x}=3,1\) \(x=9,1\) Sum \(=10\)
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