Question

已知三角形三边长为n,n-1,n+1,当n为何值时,该三角形为直角三角形?

Answer 1

(n+1)^2-(n-1)^2=n^2

(n+1+n-1)(n+1-n+1)=n^2

4n=n^2

n^2-4n=0

n^2-4n+4=4

(n-2)^2=4

∵n-2>0

∴n-2=2

n=4