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Ratio Resolution (Posted on 2011-06-15) Difficulty: 2 of 5
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

No Solution Yet Submitted by K Sengupta    
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re(2): answers only- spoiler | Comment 4 of 6 |
(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
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