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Question

Quantitative Aptitude Question on Linear Equations in One Variable

For real xx, the maximum possible value of x1+x4\frac{x}{\sqrt{1+x^4}} is

A

13\frac{1}{\sqrt3}

B

1

C

12\frac{1}{\sqrt2}

D

12\frac{1}{2}

Answer

12\frac{1}{\sqrt2}

Explanation

Solution

The correct is (C): 12\frac{1}{\sqrt2}

x1+x4=11x2+x2\frac{x}{\sqrt{1+x^4}}=\frac{1}{\sqrt{\frac{1}{x^2}}}+x^2

x2+1x2≥2x^2+\frac{1}{x^2}≥2

Hence the maximum value of is 12\frac{1}{\sqrt2}