Published by:
CGP EDU Academic Team
Published on: August 13, 2026
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 = x 2 + x + 1, b = x 2 – 1 and c = 2x + 1 is (are)
A
– 
B
1 + 
C
2 + 
D
4 
Text Solution
Verified by ExpertsThe correct answer is:
B
cos 
= 
= 
= 
⇒ 
= 
⇒ 
(x 2 + x + 1) = 2x 2 + 2x – 1
⇒ ( 
– 2) x 2 + ( 
– 2) x + ( 
+ 1) = 0
on solving
x 2 + x – 
= 0 we get
x = 
+ 1, – 
At x = – 
, Side c becomes negative.
∴ x = 
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Given an isosceles triangle, whose one angle is 120° and radius of its incircle is unit. Then the …
Internal bisector of ∠ A of triangle ABC meets side BC at D. A line drawn through D perpendicular t…
If the angle A, B and C of a triangle are in arithmetic progression and if a, b and c denote the le…
Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, …
Let PQR be a triangle of area Δ with a = 2, b = and c = , where a, b and c are the lengths of the…
In a triangle PQR, P is the largest angle and cosP = . Further the incircle of the triangle touche…