JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \( \alpha \) and \( \beta \) \( (\alpha < \beta) \) are the roots of the equation \( (-2+\sqrt{3})(|\sqrt{x}-3|) + (x-6\sqrt{x}) + (9-2\sqrt{3}) = 0 \), \( x \ge 0 \), then \( \sqrt{\frac{\beta}{\alpha}} + \sqrt{\alpha\beta} \) is equal to:
- A 8
- B 9
- C 10
- D 11
Answer & Solution
Correct Answer
(C) 10
Step-by-step Solution
Detailed explanation
\((x-6 \sqrt{x}+9)-(2-\sqrt{3})|\sqrt{x}-3|-2 \sqrt{3}=0\) \(\Rightarrow|\sqrt{ x }-3|^2-(2-\sqrt{3})|\sqrt{ x }-3|-2 \sqrt{3}=0\) \(\Rightarrow|\sqrt{ x }-3|=2\) or \(|\sqrt{ x }-3|=-\sqrt{3}\) (not possible) \(\Rightarrow \sqrt{ x }=1\) or 5 \(\Rightarrow x=1\) or 5…
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