(x+\sqrt{x^{3}-1})^{5}+(x-\sqrt{x^{3}-1})^{5} is a polymonial of degree

  • Option 1)

    5

  • Option 2)

    6

  • Option 3)

    7

  • Option 4)

    8

 

Answers (1)

As we learnt inn concept

Properties of Binomial Theorem -

\left ( x+a \right )^{n}+\left ( x-a \right )^{n}= 2\left ( ^{n}c_{0} \, x^{n}+ ^{n}c_{2}\, x^{n-2}\, a^{2}+---\right )

- wherein

Sum of odd terms or even Binomial coefficients

 

 (x+\sqrt{x^{3}-1})^{5}+ (x-\sqrt{x^{3}-1})^{5}

=> 2\left [ x^{5}+{5}C_2 x^{3}\({x^{3}-1}) +{5}C_4 x^{1}(x^{3}-1)^{2} \right ]

The degree of this polynomial is 7. 

 


Option 1)

5

Incorrect option

Option 2)

6

Incorrect option

Option 3)

7

Correct option

Option 4)

8

Incorrect option

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