3 rd 3^\text{rd} of day

Algebra Level 3

Find the coefficient of the term that doesn't have x x in the expansion of

( x 4 + 1 x 10 ) 7 . \left(\sqrt[4]{x}+\frac{1}{\sqrt[10]{x}}\right)^7.


The answer is 21.

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1 solution

Paola Ramírez
Feb 26, 2015

Let ( 7 n ) x n 4 x 7 n 10 \binom{7}{n} x^{\frac{n}{4}} x^{\frac{7-n}{-10}} the term which has no x x so n 4 = 7 n 10 n = 2 \frac{n}{4}=\frac{7-n}{-10} \Rightarrow n=2

\therefore the coefficient is ( 7 2 ) = 21 \boxed{\binom{7}{2}=21}

wahhhhhhh i dont know it

Lesterjohn Casinillo - 6 years, 3 months ago

according to your solution n=2 would give (1/2) + (1/2) for power of x which is 1. which does not remove x.

Faisal Basha - 6 years, 3 months ago

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It is corrected, thanks

Paola Ramírez - 6 years, 3 months ago

but 5 should be multiplied to 21. please check.

Rajit Das - 6 years, 3 months ago

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