已知a是方程x的平方减2013x加1等于0求代数式a的平方减2012a加a的平方加1分之2013的值
\u5df2\u77e5a\u662f\u65b9\u7a0bx\u7684\u5e73\u65b9\u51cf2014x\u52a01\u7b49\u4e8e0\u7684\u4e00\u4e2a\u6839\uff0c\u6c42\u4ee3\u6570\u5f0fa\u5e73\u65b9\u51cf2013a\u52a0a\u5e73\u65b9\u52a01\u5206\u4e4b201\u2235a\u662f\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0bx\u7684\u5e73\u65b9-2014x+1=0\u7684\u89e3
\u2234a²-2014a+1=0
\u2234a²+1=2014a
\u2234a²-2013a+2014/(a²+1)
=a²-2013a+2014/(2014a)
=a²-2013a+1/a
=a-1+1/a
=(a²-a+1)/a
=2013a/a
=2013
\u662f\u5426\u53ef\u4ee5\u89e3\u51b3\u60a8\u7684\u95ee\u9898\uff1f
\u56e0\u4e3aa\u662f\u65b9\u7a0bx\u7684\u5e73\u65b9-2013x+1\u7b49\u4e8e0\u7684\u4e00\u4e2a\u6839
\u6240\u4ee5a^2-2013a+1=0\uff0c
\u6240\u4ee5a^2-2012a=a-1
a^2+1=2013a,
\u4ee3\u4eba\uff0c\u5f97\uff0c
a\u7684\u5e73\u65b9-2012a+\uff08a\u7684\u5e73\u65b9+1\u5206\u4e4b2013)
=a^2-2012a+2013/(a^2+1)
=a-1+2013/2013a
=a-1+1/a
=a+(1/a)-1
\u5c06a^2-2013a+1=0\u4e24\u8fb9\u540c\u9664\u4ee5a,\u5f97\uff0c
a-2013+1/a=0,
\u6574\u7406a+1/a=2013
\u6240\u4ee5\u539f\u5f0f=2013-1=2012
∴a²-2013a+1=0
∴a²+1=2013a a²-2012a=a-1 a²-a+1=2012a
∴a²-2012a+2013/(a²+1)
=a-1+2013/2013a
=a-1+1/a
=(a²-a+1)/a
=2012a/a
=2012
是否可以解决您的问题？
绛旓細x=a浠ｅ叆鏂圭▼锛歛²-2013a+1=0 绛夊紡涓よ竟鍚岄櫎浠 a-2013 +1/a=0 a+1/a=2013 a²+1/a²=(a+1/a)²-2=2013²-2=4052167
绛旓細=(a^2+1)/a-1 =2013-1 =2012.
绛旓細a鏄柟绋媥^2-2013x+1=0"鐨勪竴涓牴 a^2-2013a+1=0 鎵浠 a^2=2013a-1 a^2+1=2013a 鎵浠^2-2012a+2013/(a^+1)=2013a-1+2012a+2013/(2013a)=a-1+1/a=(a^2-a+1)/a=(2012a)/a=2012
绛旓細棰樼洰鏈夐棶棰橈紝鐪嬬湅鏄笅闈㈢殑鎯呭喌鍚楋紵瑙:鈭a鏄柟绋媥²-2013x+1=0鐨勪竴涓牴 鈭碼²-2013a+1=0 鈭碼²=2013a-1 鈭碼²-2014a+(a²+1)/2013 =2013a-1-2014a+(2013a-1+1)/2013 =-a-1+a =-1.
绛旓細绠鍗
绛旓細a鏄柟绋媥^2-3x+1=0鐨勬牴锛屾墍浠^2-3a+1=0,浜庢槸a^3-4a^2+4a-1=(a^2-3a+1)(a-1)=0.
绛旓細鐢遍鎰忓緱锛a骞虫柟-2013a+1=0锛屽垽鍒紡锛0.淇╄竟鍚岄櫎浠锛屽緱a+a鍒嗕箣1=2013.鍙堟湁锛宎骞虫柟-2013a=-1锛屾墍姹傚紡瀛=a+a鍒嗕箣1=2013
绛旓細鏍规嵁棰樻剰鐭ラ亾锛屽皢a浠ｅ叆鏂圭▼寰楀埌锛歛^2-a-2013=0 a^2=a+2013 a^3=a^2+2013a 鏍规嵁闊﹁揪瀹氱悊鍙煡锛歛+b=1 a^3+2014b-1013 =a^2+2013a+2014b-2013 =a+2013+2013a+2014b-2013 =2014a+2014b =2014(a+b)=2014 a^3琛ㄧず a鐨勭珛鏂 a^2琛ㄧずa鐨勫钩鏂 ...
绛旓細x²+x-2013=0 鍥犱负a 鏄柟绋嬬殑涓涓疄鏁版牴锛屾墍浠ワ紝a²+a-2013=0 鍗筹細a²+a=2013 2a²+2a=4026 a²+a-2013=4026-2013 a²+a-2013=2013
绛旓細a鏄涓鍏冧簩娆鏂圭▼ x鐨勫钩鏂-3x+1=0 鐨勬牴 a^2-3a+1=0 a-3+1/a=0 a+1/a=3 (a+1/a)^2=9 a^2+2+1/a^2=9 a^2+1/a^2=7,2,a+(1/a) = 3 (a^2)+(1/a^2) = 9 -2 = 7,1,
