Question

find the greatest angle of the triangle given sides a=x^2+3x+3,b=x^2+2x,c=2x+3​

Answer 1

Answer:

Let a=x

2

−1;b=2x+1,c=x

2

+x+1

Here the greatest side is c=x

2

+x+1

The greatest angle C will be opposite the greatest side.

c=x

2

+x+1

Use the cosine rule

⇒c

2

=a

2

+b

2

−2bc.cosC

⇒(x

2

+x+1)

2

=(x

2

−1)

2

+(2x+1)

2

−2(x

2

−1)(2x+1)cosC

⇒2(x

2

−1)(2x+1)cosC=[(x

2

−1)

2

−(x

2

+x+1)

2

]+(2x+1)

2

⇒2(x

2

−1)(2x+1)cosC=(x

2

−1+x

2

+x+1)(x

2

−1−x

2

−x−1)+(2x+1)

2

⇒2(x

2

−1)(2x+1)cosC=x(2x+1)(−2−x)+(2x+1)

2

⇒2(x

2

−1)cosC=x(−2−x)+(2x+1)=−x