Properties of TriangleHard
Question
Let ABC be a triangle such that ∠ACB = 
and let a, b and c denote the lengths of the sides opposite to A,B and C respectively. The value(s) of x for which a = x2 + x + 1, b = x2 - 1 and c = 2x + 1 is (are)
and let a, b and c denote the lengths of the sides opposite to A,B and C respectively. The value(s) of x for which a = x2 + x + 1, b = x2 - 1 and c = 2x + 1 is (are)Options
A.−(2 + √3)
B.1 + √3
C.2 + √3
D.4√3
Solution
Using cosine rule for ∠C
⇒ (√3 - 2)x2 + (√3 - 2)x + (√3 +1) = 0
⇒ x =
⇒ x = - (2 + √3), 1 + √3 ⇒ x = 1 + √3 as (x > 0).
⇒ (√3 - 2)x2 + (√3 - 2)x + (√3 +1) = 0
⇒ x =
⇒ x = - (2 + √3), 1 + √3 ⇒ x = 1 + √3 as (x > 0).
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