If the fourth term in the expansion of {√ 1/x^1+logx+x^1/12}^6 s equal to 200 and x > 1. Then find x

Question

If the fourth term in the expansion of \(\Bigg\{\sqrt{\frac{1}{x^1+log x}+x^{\frac{1}{12}}}\Bigg\}^6\)  is equal to 200 and x > 1. Then find x

Answer 1

Given, T₄ = 200 ⇒ T_{3 + 1} = 200

⇒ y² + 3y – 4 = 0

⇒ (y + 4) (y – 1) = 0

⇒ y = 1, – 4 

⇒ log₁₀ x = 1, – 4 

⇒ x = 10 [∴ log₁₀ x = - 4 ⇒ x = 10^{– 4} < 1]