If `x= (sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrt(a-2b))`, then show that `bx^2-ax+b=0`

If x = (sqrt(a+2b) + sqrt(a-2b))/(sqrt(a+2b) -sqrt(a-2b)) then prove that bx^2 -ax + b =0

If x = (sqrt(a^2+b^2)+sqrt(a^2-b^2))/(sqrt(a^2+b^2)-sqrt(a^2-b^2)) show that b^2x^2-2a^2x+b^2 =0 .

If (sqrt(a + 2b) + sqrt(a - 2b))/(sqrt(a + 2b) - sqrt(a - 2b)) = sqrt3 and a^(2) + b^(2) = 1 , then the find values of a and b. (b) If sqrt((x - sqrt(a^(2) - b^(2)))^(2) + y^(2)) + sqrt((x + sqrt(a^(2) - b^(2)))^(2) + y^(2)) = 2a then prove that (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1

Evaluate : int (dx)/(sqrt(ax+b)+sqrt(ax-b))

If 2x = sqrt((a)/(b)) - sqrt((b)/(a)) , then show that (2a sqrt(1 + x^(2)))/(x + sqrt(1 + x^(2))) = a + b

If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/((sqrt(a-x)+sqrt(x-b)) ,then (dy)/(dx) wherever it is defined is (a) (x+(a+b))/(sqrt((a-x)(x-b))) (b) (2x-a-b)/(2sqrt(a-x)sqrt(x-b)) (c) -((a+b))/(2sqrt((a-x)(x-b))) (d) (2x+(a+b))/(2sqrt((a-x)(x-b)))

Rationalise the denominator: (a) (1)/(root(3)(3) + root(3)(2)) , (b) (2)/(sqrt5 + sqrt3 + sqrt2) , (c) (x^(2))/(sqrt(x^(2) + y^(2)) - y) , (d) (1)/(sqrt6 + sqrt5 - sqrt11) (e) (sqrt(x + 2y) - sqrt(x -2y))/(sqrt(x + 2y) + sqrt(x - 2y)) , (f) (sqrt10 + sqrt5 - sqrt3)/(sqrt10 - sqrt5 + sqrt3)

"If "y=(2)/(sqrt(a^(2)-b^(2))){tan^(-1)(sqrt((a-b)/(a+b))tan""(x)/(2))}," then show that "(d^(2)y)/(dx^(2))=(b sin x)/((a+b cos x)^(2)).

If y=sqrt((a-x)(x-b))-(a-b)tan^-1sqrt((a-x)/(x-b)) ,show that dy/dx=sqrt((a-x)/(x-b))