Question

The greatest angle of the triangle whose sides are

x² + x + 1, 2x +1 and x² –1

• A. 120⁰
• B. 90⁰
• C. 60⁰
• D. 135⁰

Answer 1

Answer: (A)

120⁰

Answer 2

Since sides are positive,

∴ x² –1 > 0; (x –1) (x + 1) > 0

But when x < –1 then 2x + 1 < 0 so x > 1 only.

Also for x > 1, $\underbrace { x ^ { 2 } + x + 1 } _ { \text {say a } }$ >

Also a >

So x² + x + 1 is the greatest sides A is greatest angle.

cos A = = $\frac { - 1 } { 2 }$

⇒ A = 120⁰