`x^2 + y^2 = 25` , `x^3 + y^3 = 91`

Factorise: 49 (2x + 3y) ^(2) - 70 ( 4x ^(2) - 9 y ^(2)) + 25 ( 2 x - 3y ) ^(2)

If x + y = 7 and x^2 + y^2 = 25 , then which one of the following equals the value of x^3 + y^3 ?

{:("Column" A ,, "Column" B), (225x^(2) - 625 y^(2) = ,, (a) 25(x-2) (x-2)), (x^(2) - x - y - y^(2) = ,, (b) 25(3x- 5y) (3x + 5y)), (x^(2) - x - y^(2) + y = ,, (x + y) (x - y- 1)), (25x^(2) - 100 x + 100 = ,, (d) (x - y) (x + y -1)), (,,(e) (x + y) (x + y - 1)):}

Identify the type of conic section for each of the equations 1. 2x^(2) -y^(2) = 7 2. 3x^(2) +3 y^(2) -4x + 3y + 10 =0 3. 3x^(2) + 2y^(2) = 14 4. x^(2) + y^(2) + x-y=0 5. 11x^(2) -25y^(2) -44x + 50y - 256 =0 6. y^(2) + 4x + 3y + 4=0

Group the like terms together : 12x, 12, 25x,-25, 25y, 1, x, 12y, y, 25xy, 5x^2y , 7 xy^2 , 2xy, 3xy^2 , 4x^2y

Factorize : ( 2x + 3y )^2 + 2 (2x + 3y ) ( x + y ) + ( x + y )^2

if x^(2) + y^(2)= 25xy , then prove that 2 log(x + y) = 3log3 + logx + logy.

If x^(4) + x^(2) y^(2) + y^(4) = 91 and x^(2) - xy + y^(2) = 13 , then what is the value of | x-y|?