`x=(sqrt(b^2+a b)+sqrt(b^2-a b))/(sqrt(b^2+a b)-sqrt(b^2-a b)),t h e n f i n d t h e v a l u e o fa x^2-2t`

If x=(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrt(a-2b)) then bx^(2)+b =

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 y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)),t h e n(dy)/(dx)i se q u a lto (a y)/(xsqrt(a^2-x^2)) (b) (a y)/(sqrt(a^2-x^2)) (a y)/(xsqrt(a^2-x^2)) (d) none of these

If y=sqrt((a-x)(x-b))- (a-b)tan^(-1)sqrt((a-x)/(x-b)),t h e nfin d(dy)/(dx)dot

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

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

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 y=sqrt((a-x)(x-b))- (a-b)tan^(-1)sqrt((a-x)/(x-b)),t h e n d(dy)/(dx) is equal to'

If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h e n a is e q u a l 1/3 (b) 2/3 (c) -1/3 (d0 -2/3

If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h e n a is e q u a l 1/3 (b) 2/3 (c) -1/3 (d0 -2/3