geometry

posted by Ashley

Prove that a triangle with sides : x^2-1, 2x, and x^2 +1 is a right triangle. i substituted the "x"s with 2 and got 5, 4, and 3 and i said that because of the common pythagorean triplets this triangle is a right trianlg is there another way to prove this is a right triangle

1. Reiny

You have shown it for a specific case, but that does not prove it in general.
Why don't we just do it
It appears that x^2 + 1 is the largest side, then
is (x^2 - 1)^2 + (2x)^2 = (x^2 + 1)^2 ????

Left side
= x^4 - 2x^2 + 1 + 4x^2
= x^4 + 2x^2 + 1

Right side
= x^4 + 2x^2 + 1 = Left Side

done!

2. Anonymous

thanks now it makes so much more sense! :)

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