[" 6.If "x,y,z>0." Then show that "(x+y+z)],[((1)/(x)+(1)/(y)+(1)/(z))>=9]

If x,y,z gt 0 then prove that (x+y+z)(1/x+1/y+1/z) geq 9

Show that : (x-y) (x+y) +(y-z)(y+z)+(z-x)(z+x)=0.

If x+y+z=a , show that (1/x+1/y+1/z)^-1ge9/a

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.

x+y+z = 15 if 9, x,y,z,a are in A.P., while (1)/( x) + ( 1)/( y) + ( 1)/( z) = ( 5)?( 3) if 9, x,y,z,a are in H.P., then the value of a will be :

If x+y+z=1 and x ,y ,z are positive, then show that (x+1/x)^2+(y+1/y)^2+(z+1/z)^2>(100)/3

If x+y+z=0 then show that abs((1,1,1),(x,y,z),(x^3,y^3,z^3)) = 0.

If the arithmetic mean of y and z be x and that of (1)/(x) and (1)/(y) be (1)/(z) , then show that x, y, z are in G.P.

if x+y+z=0 , then show that, |{:(1,1,1),(x,y,z),(x^3,y^3,z^3):}|=0

If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)(y z+1)/(z y-z)+cot^(-1)(z x+1)/(z-x)