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Question

If log10(x3+y3)log10(x2+y2xy)2 where x, y are positive real numbers Then the maximum value of xy is

A
2500
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B
3000
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C
1200
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D
3500
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Solution

The correct option is A 2500
log10(x3+y3)log10(x2+y2xy)2log10(x3+y3)(x2+y2xy)log10100(x3+y3)(x2+y2xy)100(x+y)(x2+y2xy)(x2+y2xy)100 x+y100Sincemaximumvalueofxyistobecalculated,wewillassumex+y=100Themaximumofxywhenx+y=100isobtainedonlywhenx=y=50.Hence,xy=2500.

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