If `a^(x-1)=bc,b^(y-1)=ca,c^(z-1)=ab,` and `(xy+yz+zx)/(xyz)=k,` then find `K`

If a^(x-1)=bc,b^(y-1)=ca,c^(z-1)=ab, then sum((1)/(x))=

If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi , then 1/(xy)+1/(yz)+1/(zx)=

if x+y+z=1 and xy+yz+zx=1/3 then find x:y:z

If 3 rational numbers x^(1//x) , y^(1//y) and z^(1//z) are equal and x^(yz)+y^(zx)+z^(xy)=729 , then find the value of x^(1//x)

If a^(x)=b^(y)=c^(z) and abc=1 then find the value of xy+yz+zx

If a^(x)=b, b^(y)=c, c^(z)=a , then what is the value of (1)/((xy+yz+zx))((1)/(x)+(1)/(y)+(1)/(z)) ?

If a+b=z, c+a=y, b+c=x, x^(2)+y^(2)+z^(2)=50 and xy+yz+zx=47 then find the value of a^(2)+b^(2)+c^(2)+ab+bc+ca .

If tan^(-1)x+tan^(-1)y+tan^(-1)z=(pi)/(2), prove that xy+yz+zx=1

If x=1+log_(a) bc, y=1+log_(b) ca, z=1+log_(c) ab , then (xyz)/(xy+yz+zx) is equal to

If (xy)^((a-1))=z,(yz)^((b-1))=x and (xz)^((c-1))=y, and xyz is not -1,0 or 1, then which of the following is equal to ab+bc+ca?