If `(sqrt(x-2)(x-1)(x-3)(x+3))/((x+2)(x-4))>=0` ,then ?

((2-x^(2))(x-3)^(3))/((x+1)(x^(2)-3x-4))>=0

If (2+sqrt(3))^(x^(2)-1)+(2-sqrt(3))^(x^(2)-1)=4 then x= ?

if f(x)=sqrt(x+2sqrt(2x-4))+sqrt(x-2sqrt(2x-4)) then f'(3)+f'(6)= (A) 0 (B) 1 (C) 2 (D) 1/2

If x=sqrt(3)-sqrt(2) then (1)/(x^(3))-x^(3)=

x^(2)-(sqrt(3)+1)x+sqrt(3)=0 2x^(2)+x-4=0

If Delta (x) =|{:(4x-4,(x-2)^(2),x^(3)),(8x-4sqrt(2),(x-2sqrt(2)^(2)),(x+1)^(3)),(12x-4sqrt(3),(x-2sqrt(3))^(2),(x-1)^(3)):}| then

The value of f(x,y)=((4sqrt(x^(3)y)-4sqrt(x^(3)))/(sqrt(y)-sqrt(x))+(1+sqrt(xy))/(4sqrt(xy)))^(-2)(1+2sqrt((y)/(x))+(y)/(x))^((1)/(2)) when x=9,y=0.04

lim_(x rarr 1) (sqrt(x+1)-sqrt(5x-3))/(sqrt(2x+3)-sqrt(4x+1))= _________.