If `x^(1/a)=y^(1/b)=z^(1/c)" and "xyz = 1`, then show that `a+b+c=0`.

If x^(1/a)=y^(1/b)=z^(1/c) where a,b,c are in A.P,,than show that x,y,z are in G.P.

If x^2/(by+cz)=y^2/(cz+ax)=z^2/(ax+by)=1 then show that a/(a+x)+b/(b+y)+c/(c+z)=1

If x^(2) : (by + cz) =y^(2) : (cz + ax) = z^(2) : (ax + by) = 1 , then show that a/(a+x) + b/(b+y) + c/(c+z) = 1 .

If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

If a = b^(2x) , b = c^(2y) and c = a^(2z) , show that 8xyz = 1.

If x = a - (1)/(a), y = b - (1)/(b) and z = c - (1)/(c ) and a, b, c are in G.P., then show that (x+z)/(y) = r + (1)/(r ) , where r is the common ratio of the G.P.

If x^(1/3)+y^(1/3)=z^(1/3), then {(x+y-z)^(3)+27xyz} equals a.0 b.-1 c. 1d.27

If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c-a).z(a-b)=1 .