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BITSAT 2010

Exam: BITSAT
Year: 2010
Subject: Mathematics
Chapter: Limits

BITSAT 2010 · Mathematics · Limits

The minimum value of ( (x^4+y^4+z^2)/(x y z) ) for positive real...

The minimum value of (

\frac{x^4+y^4+z^2}{x y z}

) for positive real number

x, y, z

is

Options

A\$\sqrt{2}
B(2 $\sqrt{2}$ )
C(4 $\sqrt{2}$ )
D(8 $\sqrt{2}$ )

Correct answer

B. (2 $\sqrt{2}$ )

Step-by-step solution

By A.M. (\geq) G.M. (x⁴+y⁴ \geq 2 x² y²) and (2 x² y²+z² \geq

\sqrt{8}

x y z). (\Rightarrow

\frac{x^4+y^4+z^2}{x y z} \geq \sqrt{8}

)

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