JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(S=\left\{ x : x \in R \text { and }(\sqrt{3}+\sqrt{2})^{ x ^2-4}+(\sqrt{3}-\sqrt{2})^{ x ^2-4}=10\right\} \text {. }\) Then \(n ( S )\) is equal to
- A \(2\)
- B \(4\)
- C \(6\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(4\)
Step-by-step Solution
Detailed explanation
Let \((\sqrt{3}+\sqrt{2})^{ x ^2-4}= t\) \(t +\frac{1}{ t }=10\) \(\Rightarrow \quad t =5+2 \sqrt{6}, 5-2 \sqrt{6}\) \(\Rightarrow \quad (\sqrt{3}+\sqrt{2})^{ x ^2-4}=5+2 \sqrt{6}, 5-2 \sqrt{6}\) \(\Rightarrow \quad x ^2-4=2,-2 \quad \text { or } x ^2=6,2\)…
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