已知:在△ABC中,∠A∠B∠C对边是a,b,c,a=n²-1,b=2n,c=n²+1(n>1)求证∠c=90° 急——

已知:在△ABC中,∠A∠B∠C对边是a,b,c,a=n²-1,b=2n,c=n²+1(n>1)求证∠c=90° 急——
已知:在△ABC中,∠A∠B∠C对边是a,b,c,a=n²-1,b=2n,c=n²+1(n>1)求证∠c=90° 急——

已知:在△ABC中,∠A∠B∠C对边是a,b,c,a=n²-1,b=2n,c=n²+1(n>1)求证∠c=90° 急——
c^2=(n^2+1)^2=n^4+2n^2+1
a^2=(n^2-1)^2=n^4-2n^2+1
b^2=(2n)^2=4n^2
a^2+b^2=n^4-2n^2+1+4n^2=n^4+2n^2+1=c^2
∴∠c=90°