The term independent of x in the expansion of x + 1 x 2 / 3 - x 1 / 3 + 1 - x - 1 x - x 1 / 2 10 , x ≠ 1 , is equal to ___.

Question

The term independent of x in the expansion of x + 1 x 2 / 3 - x 1 / 3 + 1 - x - 1 x - x 1 / 2 10 , x ≠ 1 , is equal to ___.,

MARKS App · Accepted Answer

Given x + 1 x 2 / 3 - x 1 / 3 + 1 - x - 1 x - x 1 / 2 10 ⇒ x 1 / 3 + 1 - x + 1 x 10 ⇒ x 1 / 3 - x - 1 / 2 10 General term is T r + 1 = 10 C r x 1 / 3 10 - r - x - 1 / 2 r ∴ 10 - r 3 - r 2 = 0 ⇒ 20 - 2 r - 3 r = 0 ⇒ r = 4 Then, T 5 = C 4 10 = 10 × 9 × 8 × 7 4 × 3 × 2 × 1 = 210

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