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Question

If log10(x3+y3)log10(x2xy+y2)2 x>0, y>0, then the maximum value of x+y is

A
50
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B
100
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C
2500
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D
1200
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Solution

The correct option is B 100
For the inequality to be defined,
x3+y3>0 and x2xy+y2>0

log10(x3+y3)log10(x2xy+y2)2
log10(x3+y3x2xy+y2)2log10(x+y)2x+y100
Maximum value of x+y is 100.

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