在实数范围内因式分解，要具体过程，谢谢
\u5728\u5b9e\u6570\u8303\u56f4\u5185\u56e0\u5f0f\u5206\u89e31\uff092x²+3x-6
\u6709\u4e24\u79cd\u65b9\u6cd5
\uff081\uff09\u6c42\u6839\u6cd5
\u5bf9\u4e8e\u5173\u4e8ex\u7684\u65b9\u7a0bax²+bx+c=0\uff0c\u82e5x1\uff0cx2\u662f\u5176\u4e24\u6839
\u90a3\u4e48ax²+bx+c=a(x-x1)(x-x2)
\u8bbe2x²+3x-6=0\uff0c
\u89e3\u5f97\uff0cx1=\u3010(-3+\u221a57)/4\u3011\uff0cx2=\u3010(-3-\u221a57)/4\u3011
\u6240\u4ee52x²+3x-6= 2[x-\u3010(-3+\u221a57)/4\u3011][x-\u3010(-3-\u221a57)/4\u3011]
\uff082\uff09\u914d\u65b9\u6cd5
2x²+3x-6
=2[x²+(3/2)x-3]
=2[x²+(3/2)x+(3/4)²-(57/16)]
=-[x²-2\u00d7(3/4)\u00d7x+(3/4)²-(\u221a57/4)²]
=-\u3010[x-(3/4)]²-(\u221a57/4)²\u3011
=-[x-(3/4)-(\u221a57/4)][x-(3/4)+(\u221a57/4)]
2\uff09-5x²+6xy+y²
\uff081\uff09\u6c42\u6839\u6cd5
\u8bbe-5x²+6xy+y²=0\uff0c\u628ay\u770b\u6210\u5e38\u6570
x1=\u3010(6+2\u221a14)/10\u3011y\uff0cx2=\u3010(6-2\u221a14)/10\u3011y
\u6240\u4ee5 -5x²+6xy+y²=-5[x-\u3010(6+2\u221a14)/10\u3011y][x-\u3010(6-2\u221a14)/10\u3011y]
\uff082\uff09\u914d\u65b9\u6cd5
-5x²+6xy+y²
=y²+6xy-5x²
=(y²+6xy+9x²)-14x²
=(y+3x)²-(\u221a14x)²
=(y+3x-\u221a14x)(y+3x+\u221a14x)
\u3010\u5e0c\u671b\u5bf9\u4f60\u6709\u5e2e\u52a9\u3011
\u5c31\u662f\u5206\u89e3\u56e0\u5f0f,\u6bcf\u4e2a\u56e0\u5f0f\u90fd\u662f\u5b9e\u6570\u4e14\u4e0d\u53ef\u518d\u5206,\u59824-2=2(2-1)=2(\u6839\u53f72+1)(\u6839\u53f72-1).(\u56e0\u4e3a\u53ef\u5206\u89e3\u4e3a\u6839\u53f7\u4e8c\u7684\u5e73\u65b9,\u4e14\u6839\u53f7\u4e8c\u662f\u5b9e\u6570)
1)x^2+3√2x-2
=(x+3√2/2)^2-13/2
=(x+3√2/2)^2-(√26/2)^2
=[(x+3√2/2)+√26/2][(x+3√2/2)-√26/2]
＝[x+√2(3+√13)/2][x+√2(3-√13)/2]
2)2x^2-4xy-3y^2
=2x^2-4xy+2y^2]-5y^2
=[√2(x-y)]^2-(√5y)^2
=[√2(x-y)+√5y][√2(x-y)-√5y]
=[√2x+(√5-√2)y][√2x-(√5+√2)y]
绛旓細5銆倄²锛4y²锛媥锛2y锛(x+2y)(x-2y)+x锛2y=(x锛2y)(x-2y+1)6銆2ax锛10ay锛5by锛峛x锛漻(2a-b)-5y(2a-b)=(x-5y)(2a-b)7銆俛²锛2ab锛媌²锛2a锛2b锛1锛(a+b)^2-2(a+b)+1=(a+b-1)^2 浜屻鍦ㄥ疄鏁拌寖鍥村唴鍥犲紡鍒嗚В 1銆倄²锛2锛(x+2)...
绛旓細鍏跺疄灏辨槸瑙ｄ竴鍏冧簩娆℃柟绋嬶紝浠や笂杩板紡瀛愮瓑浜0锛屾眰鍑瀹炴暟瑙ｅ氨鍙互浜嗐傚鏋滄湁甯,y鐨勶紝鐩存帴鍋囧畾y=1杩涜姹傝В锛岄亾鐞嗘槸鍙互閫氳繃鎹㈠厓浠=xy浣垮紡瀛愯浆鍖栦负鍙湁涓涓湭鐭ユ暟 (1) A=0.75+1/4*(17)^.5B=0.75-1/4*(17)^.5 鍘熷紡=(X-A)*(X-B)(2) A=1.25-1/4*(41)^.5B=1.25+1/4*(41...
绛旓細鎮ㄥソ锛歑鐨4娆℃柟-4 =锛坸²+2锛夛紙x²-2锛=锛坸²+2锛夛紙x+鈭2锛夛紙x-鈭2锛夊鏋滄湰棰樻湁浠涔堜笉鏄庣櫧鍙互杩介棶锛屽鏋滄弧鎰忚鐐瑰嚮鈥滈変负婊℃剰绛旀鈥濆鏋滄湁鍏朵粬闂璇烽噰绾虫湰棰樺悗鍙﹀彂鐐瑰嚮鍚戞垜姹傚姪锛岀瓟棰樹笉鏄擄紝璇疯皡瑙ｏ紝璋㈣阿銆傜瀛︿範杩涙锛
绛旓細鍏充簬鍥犲紡鍒嗚В鐨勪竴鑸楠ゅ涓嬶細鎶婁竴涓椤瑰紡鍦ㄤ竴涓寖鍥(濡瀹炴暟鑼冨洿鍐鍒嗚В锛屽嵆鎵鏈夐」鍧囦负瀹炴暟)鍖栦负鍑犱釜鏁村紡鐨勭Н鐨勫舰寮忥紝杩欑寮忓瓙鍙樺舰鍙仛杩欎釜澶氶」寮忕殑鍥犲紡鍒嗚В锛涔熷彨浣滄妸杩欎釜澶氶」寮鍒嗚В鍥犲紡銆傛妸涓涓椤瑰紡鍦ㄤ竴涓寖鍥村寲涓哄嚑涓暣寮忕殑绉殑褰㈠紡锛岃繖绉嶅紡瀛愬彉褰㈠彨鍋氳繖涓椤瑰紡鐨勫洜寮忓垎瑙ｏ紝涔熷彨浣滄妸杩欎釜澶氶」寮忓垎瑙ｅ洜寮...
绛旓細鍦ㄥ疄鏁拌寖鍥村唴鍒嗚В鍥犲紡鏄妸澶氶」寮 a0+a1x+a2x^2+...+anx^n(an鈮0)鍖栨垚:(k1*x^2+b1*x+c1)(k2*x^2+b2*x+c2)...(kn*x^2+bp*x+cp)*(x+m1)(x+m2)...(x+mq)鐨勫舰寮,浠ヤ笂鍑虹幇鐨勭郴鏁板潎鍦ㄥ疄鏁拌寖鍥村唴.浠ヤ笂涓轰唬鏁板熀鏈畾鐞,浠绘剰瀹炵郴鏁板椤瑰紡閮藉彲浠ュ寲鎴愪笂杩板舰寮.鑰岃嫢鍦ㄥ鏁拌寖鍥村唴,鍒...
绛旓細鍒嗘瀽锛氶鍏堝埄鐢ㄥ钩鏂瑰樊鍏紡鍥犲紡鍒嗚В锛鍐嶈繘涓姝ュ埄鐢ㄥ钩鏂瑰樊鍒嗚В鍗冲彲锛巃4-9=锛坅2+3锛夛紙a2-3锛=锛坅2+3锛夛紙a+3锛夛紙a-3锛夛紟鐐硅瘎锛氭棰樿冩煡鍒╃敤骞虫柟宸叕寮鍦ㄥ疄鏁拌寖鍥村唴鍥犲紡鍒嗚В锛
绛旓細瀹炴暟鑼冨洿鍐呯殑鍥犲紡鍒嗚В瑕杩涜鍒颁换涓鍥犲紡涓鸿川鍥犲紡涓烘銆傝川鍥犲紡鎸囩殑鏄簩娆¤川鍥犲紡鎴栦换浣曠殑瀹炴暟绯绘暟涓娆″洜寮忋備簩娆¤川鍥犲紡鎸囩殑鏄簩娆″椤瑰紡鏍囧噯褰㈠紡涓郴鏁板叧绯烩柍锛漛*b-4ac鈮0鐨勪簩娆″椤瑰紡锛堣繖绉嶅椤瑰紡鍦ㄥ疄鏁拌寖鍥村唴鏄棤娉曠户缁垎瑙ｄ负涓娆″洜寮忎箻绉殑锛屽彧鏈夊湪澶嶆暟鑼冨洿鍐呮秹鍙婂埌铏氭暟鎵嶈兘鍒嗚В浜嗭級銆傚湪闂涓紝鍥犱负锛2x...
绛旓細瀹炴暟鑼冨洿鍐呯殑鍥犲紡鍒嗚В锛鏄寚灏嗗椤瑰紡杞寲涓哄疄鏁版暣寮忕殑涔樼Н褰㈠紡銆備互浜屾澶氶」寮忎负渚嬶紝鑻ュ叾鍒ゅ埆寮忓ぇ浜0锛屽垯鏈変袱涓笉鍚岀殑瀹炴暟鏍癸紝鍙垎瑙ｄ负锛坸-x1锛夛紙x-x2锛夌殑褰㈠紡锛涜嫢鍒ゅ埆寮忕瓑浜0锛屽垯鏈変竴涓噸鏍癸紝鍙垎瑙ｄ负锛坸-x1锛塣2鐨勫舰寮忥紱鑻ュ垽鍒紡灏忎簬0锛屽垯鏃犲疄鏁版牴锛屾棤娉鍦ㄥ疄鏁拌寖鍥村唴鍒嗚В銆傝繖涓杩囩▼瑕佹眰鏁村紡鐨...
绛旓細鍦ㄥ疄鏁拌寖鍥村垎瑙ｅ洜寮,椤惧悕鎬濅箟,灏辨槸鏁板煙鎵╁厖鍒颁簡瀹炴暟鑼冨洿(瀹炴暟鍒嗕负鏈夌悊鏁板拰鏃犵悊鏁,姣旀湁鐞嗘暟鑼冨洿灏辨洿澶т簡)銆
绛旓細x²+xy-y²=0鍗硏²+xy+0.25y²-1.25y²=0鍗筹紙x+0.5y锛²-1.25y²=0涓嬮潰灏辨槸骞虫柟宸殑鍥犲紡鍒嗚В锛坸+0.5y锛²-锛堚垰5/2y)²=0鍗筹紙x+0.5y+鈭5/2y锛(x+0.5y-鈭5/2y)=0 ...
