因式分解：(X-1)的4次方
\u201cx\u76844\u6b21\u65b9\u52a01\u201d\u600e\u4e48\u56e0\u5f0f\u5206\u89e3x^4+1
=x^4+2x²+1-2x²
=(x²+1)²-(\u221a2x)²
=(x²+\u221a2x+1)(x²-\u221a2x+1)
\u628a\u4e00\u4e2a\u591a\u9879\u5f0f\u5728\u4e00\u4e2a\u8303\u56f4(\u5982\u5b9e\u6570\u8303\u56f4\u5185\u5206\u89e3\uff0c\u5373\u6240\u6709\u9879\u5747\u4e3a\u5b9e\u6570)\u5316\u4e3a\u51e0\u4e2a\u6574\u5f0f\u7684\u79ef\u7684\u5f62\u5f0f\uff0c\u8fd9\u79cd\u5f0f\u5b50\u53d8\u5f62\u53eb\u505a\u8fd9\u4e2a\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\uff0c\u4e5f\u53eb\u4f5c\u628a\u8fd9\u4e2a\u591a\u9879\u5f0f\u5206\u89e3\u56e0\u5f0f\u3002
\u6269\u5c55\u8d44\u6599
\u65b9\u6cd5\u603b\u7ed3\uff1a
\u63d0\u516c\u56e0\u5f0f\u6cd5
\u5982\u679c\u4e00\u4e2a\u591a\u9879\u5f0f\u7684\u5404\u9879\u6709\u516c\u56e0\u5f0f\uff0c\u53ef\u4ee5\u628a\u8fd9\u4e2a\u516c\u56e0\u5f0f\u63d0\u51fa\u6765\uff0c\u4ece\u800c\u5c06\u591a\u9879\u5f0f\u5316\u6210\u4e24\u4e2a\u56e0\u5f0f\u4e58\u79ef\u7684\u5f62\u5f0f\uff0c\u8fd9\u79cd\u5206\u89e3\u56e0\u5f0f\u7684\u65b9\u6cd5\u53eb\u505a\u63d0\u516c\u56e0\u5f0f\u6cd5\u3002
\u5404\u9879\u90fd\u542b\u6709\u7684\u516c\u5171\u7684\u56e0\u5f0f\u53eb\u505a\u8fd9\u4e2a\u591a\u9879\u5f0f\u5404\u9879\u7684\u516c\u56e0\u5f0f\u3002\u516c\u56e0\u5f0f\u53ef\u4ee5\u662f\u5355\u9879\u5f0f\uff0c\u4e5f\u53ef\u4ee5\u662f\u591a\u9879\u5f0f\u3002
\u5177\u4f53\u65b9\u6cd5\uff1a\u5728\u786e\u5b9a\u516c\u56e0\u5f0f\u524d\uff0c\u5e94\u4ece\u7cfb\u6570\u548c\u56e0\u5f0f\u4e24\u4e2a\u65b9\u9762\u8003\u8651\u3002\u5f53\u5404\u9879\u7cfb\u6570\u90fd\u662f\u6574\u6570\u65f6\uff0c\u516c\u56e0\u5f0f\u7684\u7cfb\u6570\u5e94\u53d6\u5404\u9879\u7cfb\u6570\u7684\u6700\u5927\u516c\u7ea6\u6570\u5b57\u6bcd\u53d6\u5404\u9879\u7684\u76f8\u540c\u7684\u5b57\u6bcd\uff0c\u800c\u4e14\u5404\u5b57\u6bcd\u7684\u6307\u6570\u53d6\u6b21\u6570\u6700\u4f4e\u7684\u3002
\u5f53\u5404\u9879\u7684\u7cfb\u6570\u6709\u5206\u6570\u65f6\uff0c\u516c\u56e0\u5f0f\u7cfb\u6570\u4e3a\u5404\u5206\u6570\u7684\u6700\u5927\u516c\u7ea6\u6570\u3002\u5982\u679c\u591a\u9879\u5f0f\u7684\u7b2c\u4e00\u9879\u4e3a\u8d1f\uff0c\u8981\u63d0\u51fa\u8d1f\u53f7\uff0c\u4f7f\u62ec\u53f7\u5185\u7684\u7b2c\u4e00\u9879\u7684\u7cfb\u6570\u6210\u4e3a\u6b63\u6570\u3002\u63d0\u51fa\u8d1f\u53f7\u65f6\uff0c\u591a\u9879\u5f0f\u7684\u5404\u9879\u90fd\u8981\u53d8\u53f7\u3002
\u57fa\u672c\u6b65\u9aa4\uff1a
(1)\u627e\u51fa\u516c\u56e0\u5f0f\uff1b
(2)\u63d0\u516c\u56e0\u5f0f\u5e76\u786e\u5b9a\u53e6\u4e00\u4e2a\u56e0\u5f0f\uff1b
\u2460\u627e\u516c\u56e0\u5f0f\u53ef\u6309\u7167\u786e\u5b9a\u516c\u56e0\u5f0f\u7684\u65b9\u6cd5\u5148\u786e\u5b9a\u7cfb\u6570\u518d\u786e\u5b9a\u5b57\u6bcd\uff1b
\u2461\u63d0\u516c\u56e0\u5f0f\u5e76\u786e\u5b9a\u53e6\u4e00\u4e2a\u56e0\u5f0f\uff0c\u6ce8\u610f\u8981\u786e\u5b9a\u53e6\u4e00\u4e2a\u56e0\u5f0f\uff0c\u53ef\u7528\u539f\u591a\u9879\u5f0f\u9664\u4ee5\u516c\u56e0\u5f0f\uff0c\u6240\u5f97\u7684\u5546\u5373\u662f\u63d0\u516c\u56e0 \u5f0f\u540e\u5269\u4e0b\u7684\u4e00\u4e2a\u56e0\u5f0f\uff0c\u4e5f\u53ef\u7528\u516c\u56e0\u5f0f\u5206\u522b\u9664\u53bb\u539f\u591a\u9879\u5f0f\u7684\u6bcf\u4e00\u9879\uff0c\u6c42\u7684\u5269\u4e0b\u7684\u53e6\u4e00\u4e2a\u56e0\u5f0f\uff1b
\u2462\u63d0\u5b8c\u516c\u56e0\u5f0f\u540e\uff0c\u53e6\u4e00\u56e0\u5f0f\u7684\u9879\u6570\u4e0e\u539f\u591a\u9879\u5f0f\u7684\u9879\u6570\u76f8\u540c\u3002
\u53e3\u8bc0\uff1a\u627e\u51c6\u516c\u56e0\u5f0f\uff0c\u4e00\u6b21\u8981\u63d0\u5c3d\uff0c\u5168\u5bb6\u90fd\u642c\u8d70\uff0c\u75591\u628a\u5bb6\u5b88\uff0c\u63d0\u8d1f\u8981\u53d8\u53f7\uff0c\u53d8\u5f62\u770b\u5947\u5076\u3002
(x²+1)\uff08x²-1\uff09
x四次方-4x三次方+6x²-4x+1=[(x-1)^2]^2=x^4-4x^3+6x^2-4x+1
绛旓細x鍥涙鏂-4x涓夋鏂+6x²-4x+1
绛旓細1-x鐨4娆℃柟 =(1+x²)(1-x²)=(1+x²)(1+x)(1-x)
绛旓細(x²-2x)(x²-2x+2)+1 =(x²-2x)[(x²-2x)+2]+1 =(x²-2x)²+2(x²-2x)+1 =[(x²-2x)+1]²=(x²-2x+1)²=[(x-1)²]²=(x-1)鐨4娆℃柟 鏄庣櫧璇烽噰绾筹紝鏈夌枒闂杩介棶锛佹湁鏂伴棶棰樿姹傚姪锛岃阿璋!
绛旓細X鐨4娆℃柟鍑1 =(x²-1)(x²+1锛=(x+1)(x-1)(x²+1锛
绛旓細X鐨4娆℃柟鍑涓1 鍥犲紡鍒嗚В 鎴戞潵绛 鍒嗕韩 澶嶅埗閾炬帴http://zhidao.baidu.com/question/425620630961918692 鏂版氮寰崥 寰俊鎵竴鎵 涓炬姤 3涓洖绛 #鐑# 鍥介檯娌逛环闂穿,澶у箙搴︿笅璺屾槸浣曠紭鏁?鍖垮悕鐢ㄦ埛 2014-12-07 灞曞紑鍏ㄩ儴 鏈洖绛旇鎻愰棶鑰呴噰绾 5 宸茶禐杩 宸茶俯杩< 浣犲杩欎釜鍥炵瓟鐨勮瘎浠锋槸? 璇勮 鍒嗕韩 澶嶅埗閾炬帴http:...
绛旓細(x+1)^4+(x^2-1)^2+(x-1)^4 =(x+1)^4+[(x-1)(x+1)]^2+(x-1)^4 =[(x+1)^4+2(x-1)^2(x+1)^2+(x-1)^4]-(x-1)^2(x+1)^2 =[(x+1)^2+(x-1)^2]-(x-1)^2(x+1)^2 =2X^2+2-(x^2-1)^2 =2X^2+2-(x^4-2x^2+1)=-x^4+4x^2+1...
绛旓細X鐨4娆℃柟鍑1 =(x²-1)(x²+1锛=(x+1)(x-1)(x²+1锛
绛旓細浣犲ソ锛岄鐩姹傛槸鍥犲紡鍒嗚В鍚楋紵濡傛灉鏄殑璇濊В绛斿涓嬶細x^4-1=(x^2+1)(x^2-1)=(x^2+1)(x+1)(x-1)鏈杩炵画鐢ㄤ簡2娆″钩鏂瑰樊鍏紡锛屽洜寮忓垎瑙ｈ娉ㄦ剰鍒嗚В鍒颁笉鑳藉啀鍒嗚В涓烘銆傝ˉ鍏咃細甯屾湜鎴戠殑鍥炵瓟鑳藉甯埌浣狅紝璇烽噰绾炽
绛旓細鍥犲紡鍒嗚В濡備笅锛歺^4+1 =x^4+2x^2+1-2x^2 =(x^2+1)^2-2x^2 =(x^2+1)^2-(鈭2x)^2 =(x^2+1+鈭2x)(x^2+1-鈭2x)浣跨敤鐨勬柟娉曟槸閰嶆柟銆佸钩鏂瑰樊鍏紡娉曘備竴涓暟鐨勯浂娆℃柟 浠讳綍闈為浂鏁扮殑0娆℃柟閮界瓑浜1銆傚師鍥犲涓 閫氬父浠ｈ〃3娆℃柟 5鐨3娆℃柟鏄125锛屽嵆5脳5脳5=125 5鐨2娆℃柟鏄25锛屽嵆5...
绛旓細鐢ㄥ洜寮忛櫎娉曞彲鐭,涓嶈兘鍒嗚В鎴恱+1鎴栬x-1鐨勫洜寮 鍥犳搴斿垎瑙ｆ垚涓や釜浜岄」寮忕浉涔 鐢ㄥ緟瀹氱郴鏁版硶,璁惧彲鍒嗚В鎴愶紙x^2+ax-1)(X^2+bx-1),灞曞紑銆佸綊椤瑰悗鏃犺В 璁惧彲鍒嗚В鎴愶紙x^2+ax+1)(X^2+bx+1),灞曞紑銆佸綊椤瑰緱 x^4+(a+b)x^3+(ab+2)x^2+(a+b)x+1 鍒檃+b=0 ab+2=0 瑙ｅ緱 a=卤鈭...
