Question

观察下列式子①找规律,用字母表示②证明规律③在直角三角形ABC中.角C90度,AC=39999,BC=400,快速求出A

Answer 1

①找规律(n^2-1)^2+(2n)^2=(n^2+1)^2 (n>1的整数）

②证明规律

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

=n^4-2n^2+1+4n^2

=n^4+2n^2+1

=(n^2+1)^2

=右边

3999^2+400^2

=(200^2-1)+(2*200)^2

=(200^2+1)^2

=40001^2

AB=40001