`sqrt(2x+5)+sqrt(x-1)>8`

Using properties of proportion, solve for x : (i) (sqrt(x + 5) + sqrt(x - 16))/ (sqrt(x + 5) - sqrt(x - 16)) = (7)/(3) (ii) (sqrt(x + 1) + sqrt(x - 1))/ (sqrt(x + 1) - sqrt(x - 1)) = (4x -1)/(2) . (iii) (3x + sqrt(9x^(2) -5))/(3x - sqrt(9x^(2) -5)) = 5 .

lim_(x rarr 5) (sqrt(2x-3)-sqrt(3x-8))/(sqrt(2x-1)-sqrt(3x-6))= _______.

If y=sqrt(x^2+6x+8) then show that one of the value of sqrt(1+iy)+sqrt(1-iy) is sqrt(2x+8) (i=sqrt(-1))

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

Prove that the following equations has no solutions. (i) sqrt((2x+7))+sqrt((x+4))=0 (ii) sqrt((x-4))=-5 (iii) sqrt((6-x))-sqrt((x-8))=2 (iv) sqrt(-2-x)=root(5)((x-7)) (v) sqrt(x)+sqrt((x+16))=3 (vi) 7sqrt(x)+8sqrt(-x)+15/(x^(3))=98 (vii) sqrt((x-3))-sqrt(x+9)=sqrt((x-1))

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

int_(1)^(5)(sqrt(x+2sqrt(x-1))+sqrt(x-2sqrt(x-1)))dx =