The least value of `2x^2 - 4x + 3y^2- 18y + 31` is

The least value of 2x^2+y^2+2xy+2x-3y+8 for realnumbers x and y is

The least value of 2x^(2)+y^(2)+2xy+2x-3y+8 for real number x and y is

The least value of 2x^(2)+y^(2)+2xy+2x-3y+8 for real numbers x and y is -

The equation of the normal to the curve 2x^2-xy+3y^2=18 at (3,1) is

If x>0 , y>0 and x^(2)y^(2)=6 , and if the least value of 3x+4y is P then the sum of digits in P is equal to.

The maximum value of Z = 4x + 2y subjected to the constraints 2x + 3y le 18, x + y ge 10, where x, y ge 0 is :

The maximum value of Z = 4x + 2y subject to the constraints 2x+3y le 18,x+y ge 10, x , y ge 0 is