如果2X-1的四次方=a0+a1乘X+a2乘X的二次方+a3乘X的三次方+a4乘X的四次方，则a0+a1+a2+a3+a4= a0+a2+a4= 已知（2x+1）的四次方=a0×x的四次方+a1×x的三次方...
\u82e5\uff082x-1\uff09\u7684\u4e94\u6b21\u65b9=a5x\u7684\u4e94\u6b21\u65b9+a4x\u7684\u56db\u6b21\u65b9+a3x\u7684\u4e09\u6b21\u65b9+a2x\u7684\u4e8c\u6b21\u65b9+a1x+a0\uff0c\u5219a4+a2+a0=\uff1f\u4f60\u597d\uff01\u8bf7\u95ee\u4f60\u539f\u5f0f\u4e2da5x\u3001a4x......\u7684\u6570\u5b57\u662f\u4e0b\u6807\u5417\uff1f
\u82e5\u662f\uff0c\u5219\u6b64\u9898\u5e94\u8be5\u8fd9\u6837\u89e3\uff1a
\u89e3\uff1a
\u539f\u5f0f\uff1a(2x-1)^5 = a5x^5 + a4x^4 + a3x^3 + a2x^2 + a1x + a0
\u56e0\u4e3a\u6b64\u5f0f\u4e3a\u6052\u7b49\u5f0f
\u6240\u4ee5\u4e0d\u8bbax\u7684\u503c\u4e3a\u591a\u5c11\uff0c\u539f\u5f0f\u59cb\u7ec8\u6210\u7acb
\u6240\u4ee5\u4ee4x = 1\uff0c
\u4ee3\u5165\u5f0f\u5b50\u53ef\u4ee5\u5f97\u52301 = a5 + a4 + a3 + a2 + a1 + a0
\u73b0\u5728\u8fd8\u9700\u8981\u4e00\u4e2a\u5f0f\u5b50\uff0c
\u4e8e\u662f\u4ee4x = -1
\u4ee3\u5165\u5f0f\u5b50\u53ef\u4ee5\u5f97\u5230-243 = - a5 + a4 - a3 + a2 - a1 +a0
\u4e24\u5f0f\u4e00\u52a0\uff0c\u518d\u9664\u4ee5\u4e8c\uff0c\u5373\u5f97\uff1aa4 + a2 + a0 = -122
\u7b2c\u4e8c\u95ee\u662f\u5426\u6709\u8bef
\u5f53x=1\u65f6
(2x+1)^4=a0x^4+a1x^3+a2x^2+a3x^+a4
a0+a1+a2+a3+a4=(2*1+1)^4
a0+a1+a2+a3+a4=3^4
a0+a1+a2+a3+a4=81................1\u5f0f
\u5f53x=-1\u65f6
a0-a1+a2-a3+a4=(-1*2+1)^4
a0-a1+a2-a3+a4=1............2\u5f0f
1\u5f0f+2\u5f0f\u5f97
2*(a0+a2+a4)=82,
a0+a2+a4=41
(2×1-1)的4次方=a0+a1+a2+a3+a4
∴a0+a1+a2+a3+a4=1
x=-1时
(-2-1)的4次方=a0-a1+a2-a3+a4
81=a0-a1+a2-a3+a4
∴2a0+2a2+2a4=82
∴a0+a2+a4=41
绛旓細鎶2x+1鐨4娆℃柟灞曞紑 a,b,c,d鍥涗釜鍊煎氨鍑烘潵浜 a=16 b=32 c=24 d=8 e=1 鎵浠=0 閫塁 濂藉嚑骞存病鍋氫簡 鎵浠ユ湁娌℃湁绠渚跨殑鏂规硶 灏变笉鏅撳緱浜
绛旓細1.褰揳=1鏃讹紝锛2*1-1)鐨5娆℃柟=a0+a1+a2+a3+a4+a5a0+a1+a2+a3+a4+a5=12.褰揳=-1鏃讹紝銆2*锛-1锛-1銆戠殑5娆℃柟=a0-a1+a2-a3+a4-a5a0-a1+a2-a3+a4-a5=-243
绛旓細瑙ｏ細姝ょ被闂涓鑸噰鐢ㄨ祴鍊兼硶 (2x-1)^5=a0+a1x+a2x^2+a3x^3+a4x^4+a5x^5 [1]浠=1 鍒:1=a0+a1+a2+a3+a4+a5 ---(1)[2]浠=-1 鍒欙細-3^5=a0-a1+a2-a3+a4-a5 ---(2)鍒(1)+(2)寰楋細1-3^5=2(a0+a2+a4)鏁咃細a0+a2+a4=(1/2)(1-3^5)=-121 ...
绛旓細(2x锛1)^5=a0锛媋1x锛媋2x²锛媋3x³锛嬧︼紜a5x^5 銆恱^5琛ㄧずx鐨5娆℃柟銆戣繖涓紡瀛愭槸鎭掔瓑寮忥紝鑻ヨ璁＄畻a0銆乤1銆乤2銆佲︺乤5涔嬮棿鐨勫硷紝鍙互閲囩敤璧嬪兼硶銆1銆佽嫢瑕佽绠梐0锛媋1锛媋2锛嬧︼紜a5鐨勫硷紝浣犳兂鍟婏紝閭ｅ彧瑕佺敤x=1浠ｅ叆绛夊紡灏卞彲浠ヤ簡锛2銆佽嫢瑕佽绠梐0锛峚1锛媋2锛峚3锛媋4锛峚5鐨勫硷紝閭...
绛旓細妤间笂閭ｄ簺搴旇閮界畻閿欎簡 绛旀鏄疊 鐢ㄦ帓鍒楃粍鍚堢殑鐭ヨ瘑 a锛宑锛宔鍒嗗埆鏄痻鐨4娆℃柟锛2娆℃柟鍜岄浂娆℃柟椤圭殑绯绘暟 瑕佹兂寰楀埌x鐨4娆℃柟锛屽嵆鍥涗釜2x鐩镐箻锛岃鎯冲緱鍒皒鐨2娆℃柟锛屽嵆浠4涓嫭鍙蜂腑閫変袱涓嫭鍙蜂腑鐨2x鍜屽彟涓や釜鎷彿涓殑1鐩镐箻 鎯冲埌鍒皒鐨0娆℃柟锛屽嵆4涓嫭鍙蜂腑鐨1鐩镐箻 鎵浠+c+e=2鐨4娆℃柟+锛堜粠4涓腑鍙栦袱...
绛旓細瑙ｇ瓟锛(2x-1锛変簲娆℃柟=a0+a1X+a2X骞虫埧+a3X涓夋鏂+a4X鍥涙鏂+a5X浜旀鏂广(1) 浠=0 鍒 (2*0-1)^5=a0 鈭 a0=-1 (2)浠=1 鍒 (2*1-1)^5=a0+a1+a2+a3+a4+a5 鈭 a5+a4+a3+a2+a1+a0=1^5=1
绛旓細鎴戜滑闇瑕侀櫎鍘籥0 鍗宠鐭ラ亾a0 娉ㄦ剰a0+a1x+a2x鐨勫钩鏂+a3x鐨勪笁娆+a4x鐨勫洓娆+a5x鐨勪簲娆 闄や簡a0浠ュ锛屾瘡涓兘鍚湁x 鎵浠ュ彧闇璁﹛=0 (0-1)^5=a0 a0=-1 鈭-1+a1+a2+a3+a4+a5=1 a1+a2+a3+a4+a5=-2 濡傛灉浣犺鍙垜鐨勫洖绛旓紝璇风偣鍑诲乏涓嬭鐨勨滈噰绾充负婊℃剰绛旀鈥濓紝绁濆涔犺繘姝ワ紒
绛旓細浠=1浠ｅ叆:a0+a1+a2+a3+a4+a5=1 鈭礱5=2^5=32 鈭碼0+a1+a2+a3+a4=1-32=-31
绛旓細(2x-1)^4 + (x+1)^3 = (4x^2-4x+1)^2 + (x-1)^3 = 16x^4 - 32x^3 + 24x^2 - 8x + 1 + x^3 + 3x^2 + 3x + 1 = 16x^4 - 31x^3 + 27x^2 - 5x + 2 = a4x^4 + a3x^3 + a2^x^2 + a1x + a0 a2 = 27 ...
绛旓細瑙ｆ瀽锛氫护x锛1锛屼唬鍏ワ紙2x-1锛変簲娆℃柟=a0+a1X+a2X骞虫埧+a3X涓夋鏂+a4X鍥涙鏂+a5X浜旀鏂 寰梐0+a1+a2+a3+a4+a5锛1 鍙堢敱浜岄」寮忓畾鐞嗙煡锛2x-1锛変簲娆℃柟灞曞紑鍚庣殑绗竴椤圭郴鏁癮0锛滳(5,0)*(2鐨0娆℃柟)*(-1鐨5娆℃柟)锛濓紞1 鎵浠1+a2+a3+a4+a5锛1锛峚0锛2 ...
