Find the value of k if: `xy^2k = (4xy+3y)^2 - (4xy-3y)^2`

Find the value of k, if the equation 2x^(2) + 4xy - 2y^(2) + 4x + 8y + k = 0 represents a pair of lines, Further find whether these lines are parallel or intersecting.

If 2x+3y=14 and 2x-3y=2, find the value of xy.[ Hint use (2x+3y)^(2)-(2x-3y)^(2)=24xy

(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) .

If x=(sqrt3+1)/(sqrt3-1) and xy=1 then find the value of (3x^2+5xy+3y^2)/(3x^2-5xy+3y^2)

If x=2+3i and y=2-3i then find the values of : (x^(2)+xy+y^(2))/(x^(2)-xy+y^(2))

(xy+2y)-(3xy-4y)