Question

计算：（√a+1/√a）²-(√a-1/√a)²

用两种方法解。

Answer 1

（√a+1/√a）²-(√a-1/√a)²
=【（√a+1/√a）-（√a-1/√a）】【（√a+1/√a）+（√a-1/√a）】
=2/√a×2√a
=4

追问

用两种回答

追答

（√a+1/√a）²-(√a-1/√a)²
=a+2+1/a-（a-2+1/a）
=a+2+1/a-a+2-1/a
=4

Answer 2

（√a+1/√a）²-(√a-1/√a)²
=a+1/a+2-a-1/a+2
=4
（√a+1/√a）²-(√a-1/√a)²
=(√a+1/√a+√a-1/√a)(√a+1/√a-√a+1/√a)
=4

Answer 3

（√a+1/√a）²-(√a-1/√a)²
=(a+1+2√a)/a-(a+1-2√a)/a
=[(a+1+2√a)-(a+1-2√a)]/a
=4√a/a