Two sides of a triangle are given by the roots of the equation x 2 - 2 3 x + 2 = 0 and the angle between the sides is π 3 . The perimeter of the triangle is

Step-by-step solution

Let the two sides a and b are the roots of the equation x 2 - 2 3 x + 2 = 0 . ∴ a + b = 2 3 and ab = 2 . Also, ∠ C = π 3 Using cosine rule, cosC = a 2 + b 2 - c 2 2 ab ⇒ 1 2 = a 2 + b 2 - c 2 2 ab ⇒ a 2 + b 2 - c 2 = ab ⇒ a + b 2 - c 2 = 3 ab ⇒ 2 3 2 - c 2 = 3 × 2 ⇒ c = 6 ∴ Perimeter = a + b + c = 2 3 + 6 units