TS EAMCET · Maths · Quadratic Equation
The minimum value of \(\frac{9 \cdot 3^{2 x}+6 \cdot 3^x+4}{9 \cdot 3^{2 x}-6 \cdot 3^x+4}\) is
- A -1
- B \(\frac{1}{2}\)
- C \(\frac{1}{4}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
Let \(y=\frac{9 \cdot 3^{2 x}+6 \cdot 3^x+4}{9 \cdot 3^{2 x}-6 \cdot 3^x+4}\) Put, \(3^x=t\) \(\therefore \quad y=\frac{9 \cdot t^2+6 t+4}{9 t^2-6 t+4}\) \(\Rightarrow y\left(9 t^2-6 t+4\right)=9 t^2+6 t+4\) \(\Rightarrow 9 t^2(y-1)-6 t(y+1)+(4 y-4)=0\)…
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