Factorise : `(sqrt(3)-1)x^(2)-2x-(sqrt(3)+1)`

Factorise : (2-sqrt(3))x^(2)+4x+(2+sqrt(3))

Factorise : (sqrt(2)-1)x^(2)+2sqrt(2)x+(sqrt(2)+1)

Factorise : x^(2)-sqrt(3)x-18

Factorise : 6sqrt(3)a^(2)-21a+5sqrt(3)

Factorise : x^(3)+(1)/(x^(3))-2x-(2)/(x)

Number of solutions of the equation (sqrt(3)+1)^(2x)+(sqrt(3)-1)^(2x)=2^(3x) is________

A beam of light is sent along the line x-y=1 , which after refracting from the x-axis enters the opposite side by turning through 30^0 towards the normal at the point of incidence on the x-axis. Then the equation of the refracted ray is (a) (2-sqrt(3))x-y=2+sqrt(3) (b) (2+sqrt(3))x-y=2+sqrt(3) (c) (2-sqrt(3))x+y=(2+sqrt(3)) (d) y=(2-sqrt(3))(x-1)

If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3, w h e r e|x|<1, then x is equal to 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

Factorise : x(x+1)(x+2)-3x-3

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)