为啥x1-x2的绝对值＝根下D方-4F？ 急求！！为什么x1-x2的绝对值=根号下（x1+x2）的平方...
\u4e3a\u4ec0\u4e48x1-x2\u7684\u7edd\u5bf9\u503c=\u6839\u53f7\u4e0b\u7684\u5e73\u65b9\u8fd9\u5c5e\u4e8e\u97e6\u8fbe\u5b9a\u7406\u7684\u62d3\u5c55\u3002 \u9996\u5148\u53ef\u4ee5\u7528\u4e8e\u6c42|x1-x2| \u5176\u6b21 \u5728\u89e3\u6790\u51e0\u4f55\u4e2d \u5e38\u5e94\u7528 \u5c24\u5176\u662f\u5728\u76f4\u7ebf\u548c\u66f2\u7ebf\u76f8\u4ea4\u6c42\u4ea4\u70b9\u95f4\u7ebf\u6bb5\u957f\u5ea6\u65f6\u3002
然后大概是利用二元一次方程根与系数的关系，可以得
x1+x2=D
x1x2=F
带入即可。
绛旓細|x1-x2|=鈭氾紙x1+x2锛塣2-4x1x2 鐒跺悗澶ф鏄埄鐢ㄤ簩鍏冧竴娆℃柟绋嬫牴涓庣郴鏁扮殑鍏崇郴锛屽彲浠ュ緱 x1+x2=D x1x2=F 甯﹀叆鍗冲彲銆
绛旓細鈭典袱鏍逛箣宸槸閫氳繃涓ゆ牴涔嬪拰涓庝袱鏍逛箣绉彉褰㈠緱鍒扮殑锛(X1-X2)^2=(X1+X2)^2-4X1*X2 杩欐牱锛殀X1-X2|=鈭氾蓟(X1+X2^2-4X1*X2锛斤紝灏辨湁浜嗘牴鍙枫傚彟澶栵細涓鍏冧簩娆℃柟绋嬬殑姹傛牴鍏紡涓紝涓ゆ牴鐩稿噺涔熷緱鍒板惈鏈夋牴鍙风殑寮忓瓙銆
绛旓細鍥犱负 锛坸1+x2锛夌殑骞虫柟-4x1x2=(x1鐨勫钩鏂+x2鐨骞虫柟+2x1x2)-4x1x2=x1鐨勫钩鏂+x2鐨勫钩鏂-2x1x2=(x1-x2)鐨勫钩鏂
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绛旓細|x1-x2|=鈭(x1-x2)^2=鈭(x1^2-2x1x2+x2^2)=鈭(x1^2+2x1x2+x2^2-4x1x2)=鈭歔(x1+x2)^2-4x1x2]=鈭歔(-b/a)^2-4c/a]=鈭歔(b^2-4ac)/a^2]=鈭氣柍/|a|
绛旓細浣犳槸鎯抽棶x1-x浜岀殑缁濆鍊鏄粈涔堝悧锛焫1-x浜岀殑缁濆鍊兼槸|x1-x2|=鈭(x1-x2)?=鈭歔(x1+x2)?-4x1x2]=鈭(b?/a?-4c/a)=[鈭(b?-4ac)]/|a|銆傜粷瀵瑰兼槸鎸囦竴涓暟鍦ㄦ暟杞翠笂鎵瀵瑰簲鐐瑰埌鍘熺偣鐨勮窛绂伙紝鐢ㄢ渱|鈥濇潵琛ㄧず銆
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