TS EAMCET · Maths · Basic of Mathematics
The solution set of the inequation \(3^x+3^{1-x}-4 \lt 0\) contained in \(\mathbf{R}\) is
- A \((1,2)\)
- B \((1,3)\)
- C \((0,2)\)
- D \((0,1)\)
Answer & Solution
Correct Answer
(D) \((0,1)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & 3^x+3^{1-x}-4 \lt 0 \\ \Rightarrow & 3^x+\frac{3}{3^x}-4 \lt 0 ; \operatorname{Le} t 3^x=t \Rightarrow t+\frac{3}{t}-4 \lt 0\end{aligned}\) \(\Rightarrow t^2-4 t+3 \lt 0 \quad\left[\because t=3^x \neq 0\right]\) \(\Rightarrow(t-1)(t-3) \lt 0\)…
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