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——
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![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——](/uploads/image/z/7803628-52-8.jpg?t=%E5%B7%B2%E7%9F%A5%3A%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%2C%E2%88%A0A%E2%88%A0B%E2%88%A0C%E5%AF%B9%E8%BE%B9%E6%98%AFa%2Cb%2Cc%2Ca%3Dn%26%23178%3B-1%2Cb%3D2n%2Cc%3Dn%26%23178%3B%2B1%28n%26gt%3B1%29%E6%B1%82%E8%AF%81%E2%88%A0c%3D90%C2%B0+%E6%80%A5%E2%80%94%E2%80%94)
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°