[" 143.If "x=sqrt(1+sqrt(1+sqrt(1+cdots oo)))" then the positive value of "],[x" is "]

If x=sqrt(1+sqrt(1+sqrt(1+sqrt(1+.oo))), then ) the value of x is (A)(sqrt(7)+1)/(2) (B) (sqrt(6)+1)/(2)(C)(sqrt(3)+1)/(2) (D) (sqrt(5)+1)/(2)

If x=sqrt((sqrt(5)+1)/(sqrt(5)-1)), then the value of x= of 5x^(2)-5x-1 is

If sqrt(x)+sqrt(x-sqrt(1-x))=1 then value of x is

If y=sqrt(x+sqrt(x+sqrt(+…..oo))) then prove that (2y-1)dy/dx=1.

sqrt(x)-sqrt(1-x)=(1)/(5) and sqrt(x)+sqrt(1-x)=(7a)/(5) then the value of a is :

If y=sqrt(x+sqrt(x+sqrt(x+\ dotto\ oo))) , prove that (dy)/(dx)=1/(2\ y-1)

If x= (1)/(sqrt2) + (1)/(2) + (1)/(2sqrt2) +… + oo , then find the value of x + (1)/(x) .

If y = sqrt(x+ sqrt(x + sqrt(x + ......oo))) , show that (2y - 1) (dy)/(dx) = 1

If 2x = sqrt(a) - (1)/(sqrt(a)) , then the value of (sqrt(x^(2) + 1))/(x + sqrt(x^(2) +1)) is

If y=sqrt(x+sqrt(x+sqrt(x+...to oo)),) prove that (dy)/(dx)=(1)/(2y-1)