Question

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

(I) x${}^3$ + y${}^3$ + z${}^3$ = 3xyz

(II) x${}^3$ + y${}^2$ z + yz${}^2$ = 3xyz

(III) x${}^3$ + y${}^2$ z + z${}^2$ x = 3xyz

(IV) (x + y + z)${}^3$ = 27xyz

• A. I, IV only
• B. I, II, IV only
• C. I, II and III only
• D. All of them

Answer 1

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.