AP EAMCET · Maths · Binomial Theorem
If \(t_r\) is the \(r^{\text {th }}\) term in the expansion of \(\left(2^x+4^{-x}\right)^8\) and if \(t_3=7 t_2\) then \(x=\)
- A \(\frac{1}{2}\)
- B \(-\frac{1}{2}\)
- C \(\frac{1}{3}\)
- D \(-\frac{1}{3}\)
Answer & Solution
Correct Answer
(D) \(-\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
\(t_2 = \binom{8}{1}(2^x)^7(4^{-x})^1 = 8 \cdot 2^{7x} \cdot 2^{-2x} = 8 \cdot 2^{5x}\) \(t_3 = \binom{8}{2}(2^x)^6(4^{-x})^2 = 28 \cdot 2^{6x} \cdot 2^{-4x} = 28 \cdot 2^{2x}\) \(t_3 = 7t_2 \Rightarrow 28 \cdot 2^{2x} = 7 \cdot (8 \cdot 2^{5x})\)…
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