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Question

Let x, y, z be positive reals. Which of the following implies x = y = z?

(I) x3 + y3 + z3 = 3xyz

(II) x3 + y2 z + yz2 = 3xyz

(III) x3 + y2 z + z2 x = 3xyz

(IV) (x + y + z)3 = 27xyz


A

I, IV only

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B

I, II, IV only

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C

I, II and III only

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D

All of them

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Solution

The correct option is B

I, II, IV only


For option (3) if x = z = 1 and y = 2 then option (3) is right.

So by option (3) we can’t say x = y = z. Remaining options implies x = y = z.


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