First slide

Binomial theorem for positive integral Index

Question

The expression ${(x + \sqrt{x^{3} - 1})}^{6} + {(x - \sqrt{x^{3} - 1})}^{6}$ is a polynomial of degree

Moderate

A

6
B

7
C

9
D

10

Solution

Use $(x + a)^{6} + (x - a)^{6}$
$= 2 [x^{6} +^{6} C_{2} x^{4} a^{2} +^{6} C_{4} x^{2} a^{4} +^{6} C_{6} a^{6}]$
putting $a = \sqrt{x^{3} - 1},$ we find it to be a polynomial of $9 .$

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