Step-by-step explanation:
Given : A triangle with side lengths [tex]a = x^2-1, b = 2x, \text{ and } c = x^2 + 1[/tex]
To find : Prove that when x > 1, it is a right triangle. Use the Pythagorean theorem and the given side lengths to create an equation. Use the equation to show that this triangle follows the rule describing right triangles. Explain your steps ?
Solution :
For right triangle the Pythagorean theorem is to be satisfied.
i.e. [tex]c^2=a^2+b^2[/tex]
Here, [tex]a = x^2-1, b = 2x, \text{ and } c = x^2 + 1[/tex]
Substitute the values,
[tex](x^2+1)^2=(x^2-1)^2+(2x)^2[/tex]
[tex]x^4+1+2x^2=x^4+1-2x^2+4x^2[/tex]
[tex]x^4+1+2x^2=x^4+1+2x^2[/tex]
LHS=RHS
It is a right triangle.
