Question

在△ABC中,BC=n平方-1,AC=2n,AB=n平方+1（n＞2的整数）.△ABC是直角三角形吗?说明理由.

Answer 1

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

=n^4-2n^2+1

AC^2=(2n)^2

=4n^2

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

=n^4+2n^2+1

显然,BC^2+AC^2=n^4-2n^2+1+4n^2

=n^4+2n^2+1

=AB^2

所以△ABC是直角三角形