Each of x, y and z is a positive real number.

Determine the ratio x:y:z in each of the following equations.

(I) (x+z)/y = z/x = x/(z-y)

(II) 21(x² + y² + z²) = (x + 2y + 4z)²

(In reply to re: answers only- spoiler by Charlie)

I 20x^2-4xy-8xz+17y^2-16yz+5z^2 = 0        Expanding and simplifying
II 20x^2-4x(2x)-8xz+17(2x)^2-16(2x)z+5z^2 = 0  Set y=2x
III 80x^2-40xz+5z^2 = 0     Simplifying
IV 5(z-4x)^2 = 0     Completing square
V y=2x, z=4x

is one possible method

Posted by broll on 2011-06-20 14:23:48