`ab(x^2+1)+x(a^2+b^2)`

, (a+b)^2 + (a-b)^2 = 2(a^2 + b^2) or (a+b)^2 - (a -b)^2= 4ab or ab = (frac(a+b)(2))^2 -(frac(a-b)(2))^2 to find the following. Let's find 8xy( x^2 + y^2 ) when (x+y) = 5 and (x-y) = 1

If (x+1)/(x-1)=(a)/(b) and (1-y)/(1+y)=(b)/(a), then the value of (x-y)/(1+xy) is (2ab)/(a^(2)-b^(2)) (b) (a^(2)-b^(2))/(2ab) (c) (a^(2)+b^(2))/(2ab) (d) (a^(2)-b^(2)backslash)/(ab)

Prove that the angle between the st. lines : (a + b)x + (a-b)y = 2ab and (a-b)x+(a+ b) y = 2ab is tan^-1 frac(2ab)(a^2-b^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))

The square root of x^(b^(2))x^(b^(2)+2ab)x^(a^(2)-b^(2)) is

Solve: (a - b )x + (a + b)y = a^(2) - 2ab - b^(2) and (a + b) (x + y) = a^(2) + b^(2)

Find the value of (5a^(6))x(-10ab^(2))x(-2.1a^(2)b^(3)) for a=1 and b=(1)/(2)

Factorise the using the identity a ^(2) + 2 ab + b ^(2) = (a + b) ^(2) a ^(2) x ^(2) + 2 ax +1