It depends on the value of x. If you graph y1 = x^2 + 3x + 3, y2 = x^2 + 2x, and y3 = 2x + 3, two of the graphs are parabolas and one is a straight line. On the interval [0, 1], the largest values are for y1 = x^2 + 3x + 3 and the smallest are for y2 = x^2 + 2x. For the interval [-1, 0] the order is different.utkarshakash said:Homework Statement
The sides of a triangle are [itex]x^2+3x+3, 2x+3,x^2+2x[/itex]. Prove that the greatest angle of the triangle is 120°.
Homework Equations
The Attempt at a Solution
The greatest angle is the one opposite to the greatest side. But how to decide which one is greatest side? Also the sides are variable.
No, it turns out not to.Mark44 said:It depends on the value of x.
Mark44 said:It depends on the value of x.
By what I said, I meant that the values of the three expressions depend on x. As you said, one of the sides is the longest, but for other two sides, it depends on which interval you're looking at.haruspex said:No, it turns out not to.
Proving that the greatest angle is 120 means providing evidence or demonstrating that the largest angle in a given set of angles is exactly 120 degrees.
Proving that the greatest angle is 120 is important because it helps us understand the properties and relationships of angles, which are fundamental concepts in geometry and other scientific fields.
There are several ways to prove that the greatest angle is 120, depending on the given information and context. One way is by using the Triangle Sum Theorem, which states that the sum of the interior angles in a triangle is always 180 degrees. Another way is by using the definition of a straight angle, which is 180 degrees, and the fact that the greatest angle in a triangle is opposite to the longest side.
Yes, depending on the given information and context, the greatest angle can be something other than 120. In a triangle, the greatest angle can range from 91 degrees (right triangle) to 179 degrees (acute triangle). In other geometric figures, the greatest angle can have different measures.
Proving that the greatest angle is 120 has many real-life applications, especially in fields such as architecture, engineering, and navigation. For example, in architecture and engineering, knowing the properties and relationships of angles is essential for designing and constructing structures that are stable and functional. In navigation, understanding angles is crucial for determining direction and position.