If a² x^{4} + b² y^{4} = c^{4}, then the maximum value of xy is

Correct Answer is : c22ab{c²}{{2ab}}2abc2

Correct Answer is : c22ab{c²}{{2ab}}2abc2

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BITSAT 2013 Paper

Section: Mathematics

Question : 112 of 150

Marks: +1, -0

a^{2} x^{4} + b^{2} y^{4}

c^{4}

, then the maximum value of xy is

Solution:

If the sum of two positive quantities is a constant, then their product is maximum, when they are equal.

∴

a^{2} x^{4}

b^{2}y^{2}

is maximum when

a^{2}x^{4}

b^{2}y^{4}

\frac{1}{2}

(

a^{2}x^{4}

) =

\frac{1}{2} (a^{2}x + b^{2}y^{4})

\frac{c^{4}}{2}

∴ maximum value of

a^{2}x^{4}

b^{2}y^{4}

\frac{c^{4}}{2} \cdot \frac{c^{4}}{2}

\frac{c^{8}}{4}

Maximum value of xy =

\left(\frac{c^{8}}{4a^{2}b^{2}}\right)^{\frac{1}{4}}

\frac{c^{2}}{\sqrt{2ab}}

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