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  • The expression <img alt="\small \left[x+\left(x^3-1\right)^{1 / 2}\right]^5+\left[x-\left(x^3-1\right)^{1 / 2}\right]^5" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Csmall%20%5Cleft

The expression \small \left[x+\left(x^3-1\right)^{1 / 2}\right]^5+\left[x-\left(x^3-1\right)^{1 / 2}\right]^5  is a polynomial of degree 

Option: 1

5


Option: 2

6


Option: 3

7


Option: 4

8


Answers (1)

best_answer

Given expression \begin{aligned} & =2\left[x^5+{ }^5 C_2 x^3\left\{\left(x^3-1\right)^{1 / 2}\right\}^2+{ }^5 C_4 x\left\{\left(x^3-1\right)^{1 / 2}\right\}^4\right] \\ & =2\left[x^5+10 x^3\left(x^3-1\right)+5 x\left(x^3-1\right)^2\right] \\ & =5 x^7+10 x^6+x^5-10 x^4-10 x^3+5 x \end{aligned}
which is a polynomial of degree 7 .

Posted by

shivangi.bhatnagar

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