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

If x is real, then the maximum value of y=2(a-x)(x+sqrt(x^2+b^2))

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

If sin x - sin y = a " and "cos x + cos y = b,"show that " "tan" (x+y)/2 = pm sqrt((4-a^(2)-b^(2))/(a^(2)+b^(2)))

If x is real , show that the expressions (x^2-ab)/(2x-a-b) has no real value between a and 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 a,b, are real, show that the roots of each of the following equations are real: 1/(x-a)+1/(x-b)=1/a^2

If a/b = x/y , then show that (a+b) (a^(2)+b^(2))x^(3) = (x+y)(x^(2)+y^(2))a^(3)

If x=(4ab)/(a+b) then show that (x+2b)/(x-2b)+(x+2b)/(x-2b)=2 .

IF a,b,c are real, show that the roots of each of the following equations are real: (x-a)(x-b)=b^2

If a,b, are real, then show that the roots of the equation (x-a)(x-b) = b^2 are always real.