Newton's Sums with euler's number?

Algebra Level 3

x+y+z=0x2+y2+z2=ex3+y3+z3=e2x+y+z=0\\ { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 }=e\\ { x }^{ 3 }+{ y }^{ 3 }+{ z }^{ 3 }={ e }^{ 2 }\\

This set of equations is true for three complex numbers x,y,zx, y, z, where ee is Euler's Constant.

If xyz=ABeCxyz=\frac { A }{ B } { e }^{ C } for positive integers A,B,CA,B,C with coprime A,BA,B, find A+B+CA+B+C.

Try this next.
×

Problem Loading...

Note Loading...

Set Loading...