TS EAMCET · Maths · Binomial Theorem
The number of irrational terms in the expansion of \(\left(5^{1 / 2}+7^{1 / 8}\right)^{1024}+\left(5^{1 / 2}-7^{1 / 8}\right)^{1024}\) is
- A \(896\)
- B \(129\)
- C \(513\)
- D \(384\)
Answer & Solution
Correct Answer
(D) \(384\)
Step-by-step Solution
Detailed explanation
Given expression is \(\left(5^{1 / 2}+7^{1 / 8}\right)^{1024}+\left(5^{1 / 2}-7^{1 / 8}\right)^{1024}\) Since, the \(\operatorname{LCM}\{2,8\}=8\), so the every eight term is a rational number in the expansion of \(\left(5^{1 / 2}+7^{1 / 8)^{1024}}\right.\) of…
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