" (iv) "sqrt(3x^(2)+16x+13sqrt(3))

Find the nature of the roots of the quadratic equation 13 sqrt(3)x^(2)+10x+ sqrt(3)=0

If sqrt(3x^(2)-12x + 19) + sqrt(3x^(2)-12x-11)= 16 then find sqrt(3x^(2)-12x + 19) - sqrt(3x^(2) -12x-11) = ?

The length of latusrectum of the parabola 13[(x-3)^(2)+(y-4)^(2)]=(2x-3y+5)^(2) is A) (2)/(sqrt(13)) B) (4)/(sqrt(13)) C) (1)/(sqrt(13)) D) (5)/(sqrt(13))

Show that 0le3sin sqrt(pi^2/16-x^2) le 3/sqrt(2)

Lt_(x to oo) (sqrt(3+9x^(2))+sqrt(4x^(2)-1))/(sqrt(1+16x^(2))-sqrt(9x^(2)+2))=

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 .

Show that : Lt_(x to a)(sqrt(a+2x)-sqrt(3x))/(sqrt(3a+x)-2sqrt(x))=(2)/(3 sqrt(3))