TS EAMCET · Maths · Binomial Theorem
If the set of all values of \(x\) for which the expansion of \((7-5 x)^{-\frac{2}{3}}\) valid is equal to \((-a, a)\), then \(5 a+7\) is equal to
- A 14
- B 21
- C 0
- D 12
Answer & Solution
Correct Answer
(A) 14
Step-by-step Solution
Detailed explanation
\((7-5 x)^{-\frac{2}{3}}=(7)^{-\frac{2}{3}}\left(1-\frac{5 x}{7}\right)^{-\frac{2}{3}}\) For validation, \(\left|\frac{-5 x}{7}\right| < 1 \Rightarrow-1 < \frac{5 x}{7} < 1\) \[ \Rightarrow-7 < 5 x < 7 \Rightarrow-\frac{7}{5} < x < \frac{7}{5} \] So,…
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