" Rinfy that "x^(2)+y^(3)+z-3xy=(1)/(2)

If x = 1, y = - 2 and z = 3. find the value of (i) x^(3) + y^(3) + z^3-3xyz (ii) 3xy^(4) - 15 x^(2) y + 4z

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

For a real number 'a' with |a| lt 1 , if x = a - a^(3) + a^(5)-…, y = 1+a^(2) + a^(4)+… and z = (1)/(a) + a^(3) + a^(7)+… then show that a^(2)z = xy .

Express ((x^(3)+y^(3)+z^(3)-3xyz)/((x^(2)+y^(2)+z^(2)-xy-yz-zx))) in lowest terms

If x = 1, y = 2 and z = 5, find the value of (i) 3x - 2y + 4z (ii) x^(2) + y^(2) + z^(2) (iii) 2x^(2) - 3y^(2) + z^(3) (iv) xy + yz - zx (v) 2x^(2) y - 5yz + xy^(2) (vi) x^(3) - y^(3) - z^(3)

Divide: 5x^(3)-15x^(2)+25xby5x4z^(3)+6z^(2)-zby-(1)/(2)z9x^(2)y-6xy+12xy^(2)by-(3)/(2)xy

If x + y + z = xyz , prove that (3x -x^(3))/ (1-3x^(2)) + (3y -y^(3))/(1- 3y^(2)) +(3z -z^(3))/(1- 3z^(2)) = (3x -x^(3))/(1-3x)^(2) * (3y- y^(3))/(1-3x)^(2)* (3z- z^(3))/(1-3z)^(2) .

If x+y+z=xyz , prove that: a) (3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^(2))+(3z-z^(3))/(1-3z^(2))= (3x-x^(3))/(1-3x^(2)).(3y-y^(3))/(1-3y^(2)).(3z-z^(3))/(1-3z^(2)) b) (x+y)/(1-xy) + (y+z)/(1-yz)+(z+x)/(1-zx)= (x+y)/(1-xy) .(y+z)/(1-yz).(z+x)/(1-zx)