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 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

int (x+a)sqrt(x^(2)-b^(2))dx

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

int (tan x sec^(2)xdx)/(sqrt(a^(2)+b^(2)tan^(2)x))

Two parallel lines lying in the same quadrant make intercepts a and b on x and y axes, respectively, between them. The distance between the lines is (a) (ab)/sqrt(a^2+b^2) (b) sqrt(a^2+b^2) (c) 1/sqrt(a^2+b^2) (d) 1/a^2+1/b^2

If y - mx = sqrt(a^(2) m^(2) + b^(2)) and x + my = sqrt(a^(2) + b^(2) m^(2)) , then prove that x^(2) + y^(2) = a^(2) + b^(2)

IfI=int(dx)/((a^2-b^2x^2)^(3/2)),t h e nIe q u a l (a) x/(sqrt(a^2-b^2x^2))+C (b) x/(2sqrt(a^2-b^2x^2))+C (c) (a x)/(sqrt(a^2-b^2x^2))+C (d) none of these

IF x,a,b be real , show that 4(a-x)(x-a+sqrt(a^2+b^2))cancelgta^2+b^2 .