Newton's Sums with pi?

Algebra Level 5

$x+y+z=1\\ { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }=\pi\\ { x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 }={ \pi }^{ 2 }+3{ z }^{ 2 }-3z+1\\$

This set of equations is true for three complex numbers $x, y, z$ .

If $xyz-xy=\frac { A }{ B } {\pi }^{ C }$ for positive integers $A, B, C$ and $\gcd(A,B)=1$ , then find $A+B+C$ .

First do this .

1 solution

Archit Boobna
Apr 17, 2015

Let k=z-1, then this question almost becomes Newton's Sums with euler's number?

Now just solve this question as done in the above mentioned question.