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The expression ${(\sqrt{2 x^{2} + 1} + \sqrt{2 x^{2} - 1})}^{6} + {(\frac{2}{\sqrt{2 x^{2} + 1} + \sqrt{2 x^{2} - 1}})}^{6}$ is a polynomial of degree

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a

6

b

8

c

10

d

12

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detailed solution

Correct option is A

We have,22x2+1+2x2−1=22x2+1−2x2−12x2+1−2x2−1=2x2+1−2x2−1Thus, the given expression can be written as2x2+1+2x2−16+2x2+1−2x2−16But (a+b)6+(a−b)6=2a6+6C2a4b2+6C4a2b4+b6Therefore, 2x2+1+2x2−16+2x2+1−2x2−16 =22x2+13+152x2+122x2−1+152x2+1×2x2−12+2x2−13which is a polynomial of degree 6.

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