Find all ordered triples (x,y,z) of real numbers such that `x-sqrt(yz)=42,y-sqrt(zx)=6,z-sqrt(xy)=-30`

If x,y,z are positive real numbers show that: sqrt(x^(-1)y)*sqrt(y^(-1)z)*sqrt(z^(-1)x)=1

If x,y,z are positive real numbers, prove that: sqrt(x^-1 y).sqrt(y^-1z).sqrt(z^(-1)x)=1

If x ,y ,z are positive real number, then show that sqrt((x^(-1)y) x sqrt((y^(-1)z) x sqrt((z^(-1)x) =1

Find square root of x + y + z + 2 sqrt(yz) + 2sqrt(zx) + 2sqrt(xy)

Find the least positive real number K such that for any positive real numbers x,y,z the following inequality holds x sqrt(y)+y sqrt(z)+z sqrt(x)<=K sqrt((x+y)(y+z)(z+x))

If x, y, z are distinct positive real numbers is A.P. then (1)/(sqrt(x)+sqrt(y)), (1)/(sqrt(z)+sqrt(x)), (1)/(sqrt(y)+sqrt(z)) are in

If x, y, z are distinct positive real numbers is A.P. then (1)/(sqrt(x)+sqrt(y)), (1)/(sqrt(z)+sqrt(x)), (1)/(sqrt(y)+sqrt(z)) are in

Given that x. y, z are unequal positive numbers show that 1/x+1/y+1/z ge1/(sqrt(xy))+1/(sqrt(yz))+1/(sqrt(zx)) .