If `x,y,z` are positive real numbers such that `x^(2)+y^(2)+Z^(2)=7` and `xy+yz+xz=4` then the minimum value of `xy` is

If x,y,z are positive reals such that x^(2)-y^(2)+z^(2)=7:xy+yz+zx=4 then the minimum valueof (4-(y+x)z) is (p)/(q) (where p,q are relatively prime).Find the value of (p+q)

If x.y,z are positive real numbers such that x^(2)+y^(2)+z^(2)=27, then x^(3)+y^(3)+z^(3) has

If the real numbers x, y, z are such that x^2 + 4y^2 + 16z^2 = 48 and xy + 4yz + 2zx = 24 . what is the value of x^(2) +y^(2) z^(2) =?

Factorise 4x^(2) + y^(2) + z^(2) - 4xy - 2yz + 4xz .

Factorise 4x^(2)+y^(2)+z^(2)-4xy-3yz+4xz

Given that x,y,z are positive reals such that xyz=32 . The minimum value of x^2+4xy+4y^2+2z^2 is ___________.

Given that x,y,z are positive reals such that xyz=32 . The minimum value of x^2+4xy+4y^2+2z^2 is ___________.

Given that x,y,z are positive reals such that xyz=32 . The minimum value of x^2+4xy+4y^2+2z^2 is ___________.

If x, y and z are real numbers and x+y+z =7 and xy+yz+xz=10 , then what will be greatest value of x?