(x+1)的平方可以用完全平方公式,那么三次方,四次方呢,有没有什么公示之类的呢?请告诉我。 (x+1)平方怎么算
\u5173\u4e8e\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u7684\u6570\u5b66\u9898\u89e3:a^2+1/a^2=(a+1/a)^2-2=16-2=14.
\u5206\u6790:\u9047\u5230\u6b64\u7c7b\u9898\u76ee,\u6211\u4eec\u9996\u5148\u8981\u60f3\u7684\u662f\u95ee\u9898\u4e0e\u5df2\u77e5\u6761\u4ef6\u4e4b\u95f4\u7684\u6570\u5b57\u7684\u8054\u7cfb.
\u5728\u672c\u9898\u4e2d\u5df2\u77e5a+1/a=4 ,\u800c\u95ee\u9898\u662fa^2+1/a^2 ,\u7531\u6b64\u6211\u4eec\u5c31\u53ef\u4ee5\u53bb\u60f3\u5230\u5148\u53bb\u51d1\u4e00\u4e2a(a+1/a)^2\u7b49\u4e8e\u51e0\uff0c\u663e\u7136\u662f16\uff1b
\u800c\u8981\u6c42\u7684\u662fa^2+1/a^2\uff0c\u90a3\u4e48\u6211\u4eec\u770b\u5230\u201c\uff08a+1/a)^2\u201c\u662f\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u5c55\u5f00\u6765\u5c31\u662fa^2+2+1/a^2\uff0c\u4e0e\u8981\u6c42\u7684a^2+1/a^2\u5c31\u5dee\u4e00\u4e2a2\uff0c\u6240\u4ee5\u51cf\u53bb2\u5c31\u662f\u95ee\u9898\u7684\u7b54\u6848\u4e86\u3002
\u6240\u4ee5\u505a\u6b64\u7c7b\u95ee\u9898\u7684\u65b9\u6cd5\u662f\uff1a\uff081\uff09\u89c2\u5bdf\u5df2\u77e5\u6761\u4ef6\u4e0e\u95ee\u9898\u7684\u6570\u5b57\u4e4b\u95f4\u7684\u5173\u7cfb\uff08\u662f\u5426\u53ef\u4ee5\u51d1\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u7b49\uff09\uff0c\uff082\uff09\u51d1\u597d\u516c\u5f0f\u4e4b\u540e\u628a\u5df2\u77e5\u6761\u4ef6\u4ee3\u5165\u8fdb\u53bb\uff1b\uff083\uff09\u628a\u51d1\u597d\u7684\u516c\u5f0f\u4e0e\u8981\u6c42\u7684\u95ee\u9898\u7684\u6570\u5b57\u518d\u505a\u5bf9\u6bd4\uff0c\u628a\u5dee\u5f02\u90e8\u5206\u627e\u51fa\u6765\uff1b\uff084\uff09\u5199\u7b54\u6848\u3002
(x+1)\u5e73\u65b9\u7684\u89e3\u7b54\u8fc7\u7a0b\u5982\u4e0b\uff1a
\uff08x+1\uff09²
=\uff08x+1\uff09\uff08x+1\uff09\uff08\u8fd9\u91cc\u662f\u628a\uff08x+1\uff09²\u62c6\u5f00\uff09
=x²+x+x+1\uff08\u8fd9\u91cc\u662f\u7b2c\u4e00\u9879\u91cc\u7684x+1\u5206\u522b\u76f8\u4e58\u7b2c\u4e8c\u9879\u7684x+1\uff09
\uff1dx²+2x+1
\u6269\u5c55\u8d44\u6599\uff1a
\u4e24\u6570\u548c\u7684\u5e73\u65b9\uff0c\u7b49\u4e8e\u5b83\u4eec\u7684\u5e73\u65b9\u548c\u52a0\u4e0a\u5b83\u4eec\u7684\u79ef\u76842\u500d\u3002
\uff08a+b\uff09²=a²+2ab+b²
\u4e24\u6570\u5dee\u7684\u5e73\u65b9\uff0c\u7b49\u4e8e\u5b83\u4eec\u7684\u5e73\u65b9\u548c\u51cf\u53bb\u5b83\u4eec\u7684\u79ef\u76842\u500d\u3002
\ufe59a\uff0db\ufe5a²=a²\ufe632ab+b²
\u4e09\u4e2a\u6570\u7684\u548c\u7684\u5e73\u65b9\uff1a
\uff08a+b+c\uff09²
=\uff08a+b+c\uff09\u00b7\uff08a+b+c\uff09
=a²+ab+ac+b²+ab+bc+c²+ac+bc
=a²+b²+c²+2ab+2ac+2bc
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1-\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f
(x+1)³=x³+3x²+3x+1
(x+1)^4=x^4+4x³+6x²+4x+1
......^5=1...+5...+10...+10...+5...+1
......^6=1...+6...+15...+20...+15...+6...+1
......^7=1...+7...+21...+35...+35...+21...+7...+1
......
(杨辉三角)
绛旓細X1=-1+鈭421锛孹2=-1-鈭421銆
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绛旓細(x+1)²=x²+2x+1 (x+1)³=x³+3x²+3x+1 (x+1)^4=x^4+4x³+6x²+4x+1 ...^5=1...+5...+10...+10...+5...+1 ...^6=1...+6...+15...+20...+15...+6...+1 ...^7=1...+7...+21...+35...+35...+...
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绛旓細涓嶈兘锛屽洜涓瀹屽叏骞虫柟鍏紡鏄椤瑰紡鐩镐箻銆
绛旓細1銆佷互涓婂椤瑰紡锛屾寚鐨勯兘鏄疄绯绘暟澶氶」寮忋傛墍浠ヤ笉鑳界ОA= -P^2+2PQ-Q^2涓瀹屽叏骞虫柟寮忥紝鍥犱负涓嶅瓨鍦ㄤ互P銆丵涓哄彉鍏冪殑瀹炵郴鏁板椤瑰紡B锛屼娇A=B^2銆2銆佷互涓婃墍璇村椤瑰紡锛岄兘鏄畝鍗曞彉鍏冪殑澶氶」寮忋備笉鑳介殢渚跨О涓涓唬鏁板紡鎴栦笁瑙掑嚱鏁板紡涓哄畬鍏ㄥ钩鏂瑰紡銆傗憼灏界鏈墄^2-2+1/x^2=(x-1/x)^2锛屼絾鏄洜涓鸿繖閲寈^2-...
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