The expansion $[x + (x^{3} - 1)^{1 / 2}]^{5} + [x - (x^{3} - 1)^{1 / 2}]^{5}$ is a polynomial of degree

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Solution

The correct option is C 7
Let $\sqrt{(x^{3} - 1)} = b$
$(x + b)^{5} + (x - b)^{5}$
$= 2 [x^{5} +^{5} C_{2} x^{3} . b^{2} +^{5} C_{4} . x . b^{4}]$
Now
$x . b^{4}$
$= x (x^{3} - 1)^{2}$
$= x [x^{6} - 2 x^{3} + 1]$
$= x^{7} - 2 x^{4} + x$ .
Hence the degree of the expression is 7.

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