If `x^(1//p) = y^(1//q) = z^(1//r) and xyz=1,` then the value of `p+q+r=`

If p,q, r are in G. P. and p ^( 1//x) = q ^( 1//y)= r ^( 1//z), verify whether x,y,z are in A.P. or G. P. or neither.

int (dx)/(x ^(2014)+x)=1/p ln ((x ^(q))/(1+ x ^(r)))+C where p,q r in N then the value of (p+q+r) equals (Where C is constant of integration)

int (dx)/(x ^(2014)+x)=1/p ln ((x ^(q))/(1+ x ^(r)))+C where p,q r in N then the value of (p+q+r) equals (Where C is constant of integration)

If p and q are the roots of the equation x^2 - 15x + r = 0 and. p - q = 1 , then what is the value of r?

If p, q, r, are in G.P. and p^(1/x) = q^(1/y) = r^(1/z) Verify x, y, z are in A.P or G.P or neither.

If x^3 + y^3 + z^3 = 3(1 + xyz) , P = y + z - x, Q = z + x - y and R = x + y - z, then what is the value of P^3 + Q^3 + R^3- 3PQR ?