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

If x^2 + y^2 + z^2 =2 (x-y-z) - 3, then the value of 2x - 3y + 4z is [Assume that x, y, z are all real numbers] :

(a) If x : y = 3 : 4 , then find the value of the ratio (2x + y) : ( 9x - 2y) . (b) If x : y = 5 : 4 , then find the value of the ratio (x^(2) + xy) : (x^(2) - xy) .

For real numbers x and y, let M be the maximum value of expression x^4y + x^3y + x^2 y + x y + xy^2 + xy^3 + xy^4 , subject to x + y = 3 . Find [M] where [.] = G.I.F.

Show that sin^(2)theta=(x^(2)+y^(2))/(2xy) is possible for real value of x and y only when x=y!=0

If sec theta = (2xy)/(x^2+y^2) possible? When x and y are positive real numbers.

Which of the following expressions are exactly equal in value ? 1. ( 3x - y) ^(2) - ( 5x ^(2) - 2xy) 2. (2x - y ) ^(2) 3. (2x pm y ) ^(2) - 2 xy 4. (2x +3y ) ^(2) - 2 xy