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If expression x+ 1 x^2 ,|x 0| attains is minimum value at x= , then ^3 is

Correct answer

2

Step-by-step solution

x+ 1 x^2 = x 2 + x 2 + 1 x^2 and AM GM x 2 + x 2 + 1 x^2 ( x 2 x 2 1 x^2 )^ 1 3 x 2 + x 2 + 1 x^2 ( 1 4 )^ 1 3 Minimum value of x+ 1 x^2 = [3] 1 4 and for minimum value x 2 = 1 x^2 x^3=2 Hence, ^3=2

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