JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(S\) be the set of all real roots of the equation, \(3^{x}\left(3^{x}-1\right)+2=\left|3^{x}-1\right|+\left|3^{x}-2\right| .\) Then \(\mathrm{S}\)
- A is an empty set.
- B contains at least four elements.
- C contains exactly two elements
- D is a singleton
Answer & Solution
Correct Answer
(D) is a singleton
Step-by-step Solution
Detailed explanation
Let \(3^{x}=t ; t>0\) \(t(t-1)+2=|t-1|+|t-2|\) \(t^{2}-t+2=|t-1|+|t-2|\) Case\(-I \): \(t<1\) \(t^{2}-t+2=1-t+2-t\) \(t^{2}+2=3-t\) \(t^{2}+t-1=0\) \(\mathrm{t}=\frac{-1 \pm \sqrt{5}}{2}\) \(\mathrm{t}=\frac{\sqrt{5}-1}{2}\) is only acceptable Case-II \(: 1 \leq t<2\)…
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