For `a ,x ,>0` prove tht at most one term of the G.P. `sqrt(a-x),sqrt(x),sqrt(a+x)` can be rational.

sqrt(4-sqrt(1-x))-sqrt(2-x)>0

(sqrt(a+x)+sqrt(a-x))/(sqrt(a+x)-sqrt(a-x))=b

(sqrt(x))^(2)-sqrt(x)-12=0

(x+sqrt(2))(x-sqrt(3))=0

If the terms of the A.P.sqrt(a-x),sqrt(x),sqrt(a+x) are all in integers,where a,x>0, then find the least composite value of a .

if f(x)=sqrt(x+sqrt(x+)sqrt(x+)sqrt(…oo)),

lim_(x to 0) (sqrt(a+x)-sqrt(a-x))/( x)

If 0

If 0

Prove that : int_(0)^(a) (sqrt(x))/(sqrt(x)+sqrt(a)-x)dx=(a)/(2)