Question

A^x=b^y=c^z and abc=1 then what is the value of xy+yz+zx=0

Answer 1

Let a^x=b^y=c^z=k

Therefore,

a=k^(1/x)

b=k^(1/y)

c=k^(1/z)

As abc=1

k^(1/x).k^(1/y).k^(1/z)=1

k^(1/x+1/y+1/z)= 1 or k^0( as any number to the power 0 is 1)

Comparing the powers we get

1/x+1/y+1/z=0

Or

(yz+xz+xy)/xyz=0

Or xy+yz+zx=0 hence proved :)