It's independent

Probability Level 3

Find the term independent of x x in expansion of ( x + 1 x 2 / 3 − x 1 / 3 + 1 − x − 1 x − x 1 / 2 ) 10 \left(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}}\right)^{10}


The answer is 210.

Rushikesh Jogdand by Rushikesh Jogdand , 22, India

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1 solution

Rushikesh Jogdand
Mar 21, 2016

Such problems look bizarre at first sight. But on second sight we can easily simplify it as, ( x 1 / 3 − x − 1 / 2 ) 10 \left(x^{1/3}-x^{-1/2}\right)^{10}

Whose independent term would be- ( 10 6 ) ( x 1 / 3 ) 6 × ( x − 1 / 2 ) 4 {10 \choose 6}\left(x^{1/3}\right)^{6}\times \left(x^{-1/2}\right)^{4} ⟹ coefficient of independent term = 210 \implies \text{coefficient of independent term}=\boxed{210}

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