若 x^(1/2) - x^(-1/2) = 2，求 x^(1/2) x^(-1/2)。
請詳解
2007-03-04 09:51:24 · 3 個解答 · 發問者 蛋寶寶 5 in 科學 ➔ 數學
x^(1/2) x^(-1/2) → x^(1/2) 十 x^(-1/2)。
2007-03-04 11:18:22 · update #1
(ａ＋ｂ)2＝(ａ－ｂ)2＋４ａｂ
已知 ｘ1/2－ｘ-1/2＝２，ｘ1/2*ｘ-1/2＝１
代入 (ｘ1/2＋ｘ-1/2)2＝(ｘ1/2－ｘ-1/2)2＋４ｘ1/2*ｘ-1/2
(ｘ1/2＋ｘ-1/2)2＝２2＋４*１
(ｘ1/2＋ｘ-1/2)2＝８
ｘ1/2＋ｘ-1/2＝２√２
2007-03-05 12:37:56 · answer #1 · answered by 郝思緹絲 4 · 0⤊ 0⤋
x^(1/2) - x^(-1/2) = 2，求 x^(1/2) 十x^(-1/2)
(a-b)^2 4ab=(a十b)^2
[ x^(1/2) - x^(-1/2)]^2 十4=[x^(1/2) 十x^(-1/2)]^2
4 十4=[x^(1/2) 十x^(-1/2)]^2
x^(1/2) 十x^(-1/2)=2根號2
2007-03-04 10:13:04 · answer #2 · answered by 樹枝 4 · 0⤊ 0⤋
x^(-1/2)為 x^(1/2)的倒數
x^(1/2) x^(-1/2)=x^(1/2) /x^(1/2)=1
2007-03-04 10:10:53 · answer #3 · answered by HandsomeConan2009 2 · 0⤊ 0⤋