If `2x=a+a^-1` and `2y=b+b^-1` then find the value of `xy+(sqrt((x^2-1)(y^2-1)))`

If x=1, y=2, z=-1 then find the value of z^2-2xy(x-y)

If x=9+4sqrt(5) and xy=1 , then find the value of ((1)/(x^(2))+(1)/(y^(2))) .

Find the value of xy+y^2x if x=1, y=0

If x= (sqrt5+1)/(sqrt5-1) and x = 1/y then find the value of (3x^(2) -7xy + 3y^(2))

If x= (sqrt7+sqrt3)/(sqrt7-sqrt3) and xy= 1 then find the value of (x^2-xy+y^2)/(x^2+xy+y^2) .

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 2x = a + (1)/(a) and 2y = b + (1)/(b) , then prove that xy + sqrt((x^(2) -1) (y^(2) - 1)) = (1)/(2) (ab + (1)/(ab))

If x=1+sqrt(2) and y=1-sqrt(2), find the value of (x^(2)+y^(2))

Find the value of: xy+y^2x , for x=-1 and y=1