Anybody got some challenging problems? (algebra preferred) Anything below calculus.

Guest Nov 3, 2019

#1**+1 **

Find the smallest possible value of

\(\frac{(y-x)^2}{(y-z)(z-x)} + \frac{(z-y)^2}{(z-x)(x-y)} + \frac{(x-z)^2}{(x-y)(y-z)}, \)

where x, y and z are distinct real numbers.

VooFIX Nov 3, 2019

#2**+1 **

min{(y - x)^2/((y - z) (z - x)) + (z - y)^2/((z - x) (x - y)) + (x - z)^2/((x - y) (y - z))} = 3

at (x, y, z) = (33/10, 8/5, -23/5)

Guest Nov 3, 2019