6.If `2^x = 3^y = 6^-z` show that `1/x `+ `1/y` + `1/z` = 0

If 2^x = 3^y =12^z show that 1/z= 1/y+2/x

If 2^x=3^y=6^(-z) prove that 1/x+1/y+1/z=0

If 2^x=3^y=6^(-z) find the value of (1/x+1/y+1/z)

If x+y+z=0 show that x^3+y^3+z^3=3x y z .

If x!=y!=z and |x x^2 1+x^3 y y^2 1+y^3 z z^2 1+z^3|=0 , then prove that x y z=-1 .

If (1)/(x) , (1)/(y) , (1)/(z) are A.P. show that (y+z)/(x) , (z+x)/(y) , (x+y)/(z) are in A.P.

If x,y,z gt 0 and x + y + z = 1, the prove that (2x)/(1 - x) + (2y)/(1 - y) + (2z)/(1 - z) ge 3 .

The lines x + y + z - 3 = 0 = 2x - y + 5z - 6 and x - y - z + 1 = 0 = 2x + 3y + 7z - k are coplanar then k equals

If x + y + z = 12, x^(2) + Y^(2) + z^(2) = 96 and (1)/(x)+(1)/(y)+(1)/(z)= 36 . Then find the value x^(3) + y^(3)+z^(3).

If z= x + yi and |2z + 1| = |z- 2i| , show that 3(x^(2) + y^(2)) + 4(x-y)=3