Tip:A–D to answerE for explanationV for videoS to reveal answer
The greatest angle of the triangle whose sides are x2+x+1,2x+1,x2−1 is:
- A.
150∘
- B.
90∘
- C.
135∘
- D.
120∘
(Correct Answer)
Explanation
Let the sides be a=x2+x+1, b=2x+1, and c=x2−1. The largest side is a=x2+x+1. We find the angle A opposite to side a using the Cosine Rule.
cosA=2(2x+1)(x2−1)(2x+1)2+(x2−1)2−(x2+x+1)2
After expanding and simplifying:
cosA=2(2x3+x2−2x−1)−2x3−x2+2x+1=−21
Correct Option: (d)
Explanation
Let the sides be a=x2+x+1, b=2x+1, and c=x2−1. The largest side is a=x2+x+1. We find the angle A opposite to side a using the Cosine Rule.
cosA=2(2x+1)(x2−1)(2x+1)2+(x2−1)2−(x2+x+1)2
After expanding and simplifying:
cosA=2(2x3+x2−2x−1)−2x3−x2+2x+1=−21
Correct Option: (d)
