If $a^x = y^b = z^c$ and $xyz = 1$, then $ab + bc + ca$ equals (when $a, b, c$ chosen so that $a^x \cdot b^y \cdot c^z =

Question

If $a^x = y^b = z^c$ and $xyz = 1$, then $ab + bc + ca$ equals (when $a, b, c$ chosen so that $a^x \cdot b^y \cdot c^z = 1$ identity holds):

Accepted Answer

$0$

Answer

$1$

Answer

$-1$

Answer

$abc$

If ax=yb=zca^x = y^b = z^cax=yb=zc and xyz=1xyz = 1xyz=1, then ab+bc+caab + bc + caab+bc+ca equals (when a,b,ca, b, ca,b,c chosen so that ax⋅by⋅cz=1a^x \cdot b^y \cdot c^z = 1ax⋅by⋅cz=1 identity holds):