Find all real numbers x, y, z such that 1/xy = (x/z) + 1, 1/yz = (y/x) + 1, 1/zx = (z/y) + 1
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Originally Posted by fardeen_gen Find all real numbers x, y, z such that 1/xy = (x/z) + 1, 1/yz = (y/x) + 1, 1/zx = (z/y) + 1 you are just solving 3 equations in 3 unknowns.. you can do it..
From the symmetry of the equations, try x = y = z, which gives $\displaystyle (x,y,z)=\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2} },\frac{1}{\sqrt{2}}\right)$.
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