if `x = (sqrt(3a + 2b) + sqrt(3a - 2b))/(sqrt(3a + 2b) - sqrt(3a - 2b))` prove that : `bx^(2) - 3ax + b = 0`

If x = (sqrt(a + 3b) + sqrt(a - 3b))/ (sqrt(a + 3b) - sqrt(a - 3b)) prove that : 3bx^(2) - 2ax + 3b = 0 .

If x=(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrt(a-2b)) , then prove that b ^2-ax+b=0

Express (-sqrt(3)+sqrt(-2))(2sqrt(3)-i) in the form of a + i b

An equilateral triangle whose two vertices are (-2, 0) and (2, 0) and which lies in the first and second quadrants only is circumscribed by a circle whose equation is : (A) sqrt(3)x^2 + sqrt(3)y^2 - 4x +4 sqrt(3)y = 0 (B) sqrt(3)x^2 + sqrt(3)y^2 - 4x - 4 sqrt(3)y = 0 (C) sqrt(3)x^2 + sqrt(3)y^2 - 4y + 4 sqrt(3)y = 0 (D) sqrt(3)x^2 + sqrt(3)y^2 - 4y - 4 sqrt(3) = 0

If x=(sqrt(3)-\ sqrt(2))/(sqrt(3)+sqrt(2)) and y=(sqrt(3)+\ sqrt(2))/(sqrt(3)-\ sqrt(2)) , then x^2+\ x y+y^2= (a) 101 (b) 99 (c) 98 (d) 102

Prove that the function f(x) = a sqrt(x - 1) + b sqrt(2x - 1)-sqrt(2x^(2) - 3x + 1) , where a + 2b = 2 and a, b in R always has a root in (1, 5) AA b in R

Find the values of a and b if : (2sqrt(3)+3sqrt(2))/(2sqrt(3)-3sqrt(2))=a+bsqrt(6)

If a = sqrt3, b = (1)/(2) (sqrt6 + sqrt2), and c = sqrt2 , then find angle A

(i) If x = (6ab)/(a + b) , find the value of : (x + 3a)/(x - 3a) + (x + 3b)/(x - 3b) . (ii) a = (4sqrt(6))/(sqrt(2) + sqrt(3)) , find the value of : (a + 2sqrt(2))/(a - 2sqrt(2)) + (a + 2sqrt(3))/(a - 2sqrt(3)) .

sin(A+B)=1/sqrt(2) cos(A-B)=sqrt3|2