In the expansion of (3^ -x4+3^ 5x4)^n, the sum of the binomial coefficients is 256 and four times the term with greatest binomial coefficient exceeds the square of the third term by 21n, then find 4x.

Question

Accepted Answer

Correct answer: 2. (2) 2n = 256 = 28 n = 8 (3^ -x4+3^ 5x4)^8 4 T5 = T32 + 21n 4 × 8C4 × 3^ -x4 4 3^ 5x4 4=(8C_2 3^ -x4 6 3^ 5x4 2)^2+21n 1120 × 3x/4 = (28 × 3x)2 + 21n 1120 × 3x/4 = 282 × 32x + 21 × 8 x= 12

$In the expansion of (3^{\frac{- x}{4}} + 3^{\frac{5 x}{4}})^{n}, the sum of the binomial coefficients is 256 and four times the term with greatest binomial coefficient exceeds the square of the third term by 21n, then find 4x.$

Solution

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