If the sum of $ 5^{\text {th }} $ and $ 6^{t h} $ terms is zero in the expansion of $ (x-2 y)^{10} $, then the value of $ \frac{x}{y} $ is equal to

Question

If the sum of $ 5^{\text {th }} $ and $ 6^{t h} $ terms is zero in the expansion of $ (x-2 y)^{10} $, then the value of $ \frac{x}{y} $ is equal to,

MARKS App · Accepted Answer

T 5 + T 6 = 0 ⇒ 10 C 4 x 6 - 2 y 4 + 10 C 5 x 5 - 2 y 5 = 0 ⇒ 10 ! 4 ! 6 ! x 6 + 16 y 4 = 10 ! 5 ! 5 ! x 5 × 32 y 5 ⇒ 5 6 x = 2 y ⇒ x y = 12 5 = 2 . 4

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