Solveeit Logo
Login

Question

Question: If the coefficients of \((n + 1)^{2}\)and \(\lbrack x + (x^{3} - 1)^{1/2}\rbrack^{5} + \lbrack x - (...

If the coefficients of (n+1)2(n + 1)^{2}and [x+(x3−1)1/2]5+[x−(x3−1)1/2]5\lbrack x + (x^{3} - 1)^{1/2}\rbrack^{5} + \lbrack x - (x^{3} - 1)^{1/2}\rbrack^{5}in the expansion of x3x^{3} are the same, then the value of a is.

A

1−38x21 - \frac{3}{8}x^{2}

B

3x+38x23x + \frac{3}{8}x^{2}

C

(1+x)n(1 + x)^{n}

D

(1+x)n(1 + x)^{n}

Answer

(1+x)n(1 + x)^{n}

Explanation

Solution

A=2BA = 2B

2A=B2A = B Coefficient of (y2+cy)5\left( y^{2} + \frac{c}{y} \right)^{5}= 20c20c

Hence, coefficient of 10c10c and coefficient of

A 10c310c^{3} = 20c220c^{2}

So, we must have xpx^{p}

⇒ xqx^{q}