Find the expression that represents the length of the hypotenuse of a right triangle whose legs measure m^2-n^2 and 2mn

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03-01-2018
Mathematics

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Find the expression that represents the length of the hypotenuse of a right triangle whose legs measure m^2-n^2 and 2mn

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altavistard altavistard · Answer 1 · 2018-01-12T21:09:10+01:00

altavistard altavistard

12-01-2018

(side 1)^2 + (side 2)^2 = hyp^2
[m^2-n^2]^2 + [2mn]^ = hyp^2

Then

m^4 - 2m^2n^2 + n^4 + 4m^2n^2 = hyp^2

m^4 + 2m^2n^2 + n^4 = hyp^2

Then hyp = +sqrt(m^4 + 2m^2n^2 + n^4) = +(m^2 + n^2) (answer)

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