设a、b是方程x2+x-2014=0的两个实数根,则a2+2a+b的值为( )A.2014B.2013C.2012D.201 设a,b是方程X2+X-2014=0的两个实数根,求a2+2...
\u8bbea\uff0cb\u662f\u65b9\u7a0bx2+x-2015=0\u7684\u4e24\u4e2a\u5b9e\u6570\u6839\uff0c\u5219a2+2a+b\u7684\u503c\u4e3a\uff08\u3000\u3000\uff09A\uff0e2012B\uff0e2013C\uff0e2014D\uff0e201\u2235a\u662f\u65b9\u7a0bx2+x-2015=0\u7684\u6839\uff0c\u2234a2+a-2015=0\uff0c\u5373a2+a=2015\uff0c\u2234a2+2a+b=a+b+2015\uff0c\u2235a\uff0cb\u662f\u65b9\u7a0bx2+x-2015=0\u7684\u4e24\u4e2a\u5b9e\u6570\u6839\u2234a+b=-1\uff0c\u2234a2+2a+b=a+b+2015=-1+2015=2014\uff0e\u6545\u9009C\uff0e
\u2235a\uff0cb\u662f\u65b9\u7a0bX²+X-2014=0\u7684\u4e24\u4e2a\u5b9e\u6570\u6839\uff0c
\u2234a²+a-2014=0
\u2234a²+a=2014
\u53c8\uff1a\u6839\u636e\u97e6\u8fbe\u5b9a\u7406\uff1aa+b=-1
a²+2a+b=\uff08a²+a\uff09+
\uff08a+b)
=
2014-1=2013
∴a2+a-2014=0,
∴a2+a=2014,
∴原式=2014+a+b,
∵a、b是方程x2+x-2014=0的两个实数根,
∴a+b=-1,
∴原式=2014-1=2013.
故选B.
绛旓細鈭礱锛b鏄柟绋媥2+x-2011=0鐨勪袱涓疄鏁版牴锛屸埓a+b=-11=-1锛屽苟涓攁2+a-2011=0锛屸埓a2+a=2011锛屸埓a2+2a+b=a2+a+a+b=2011-1=2010锛庢晠閫塀锛
绛旓細鐢遍鎰忓緱锛宎骞虫柟-2013a+1=0锛屽垽鍒紡锛0.淇╄竟鍚岄櫎浠a锛寰梐+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
绛旓細鈭礱鏄鏂圭▼x鐨勫钩鏂瑰噺2013x鍔1绛変簬0 鈭碼²-2013a+1=0 鈭碼²+1=2013a a²-2012a=a-1 a²-a+1=2012a 鈭碼²-2012a+2013/(a²+1)=a-1+2013/2013a =a-1+1/a =(a²-a+1)/a =2012a/a =2012 ...
绛旓細鈭礱鏄鏂圭▼x2+x-2014=0鐨勫疄鏁版牴锛屸埓a2+a-2014=0锛屸埓a2+a=2014锛屸埓鍘熷紡=2014+a+b锛屸埖a銆b鏄柟绋媥2+x-2014=0鐨勪袱涓疄鏁版牴锛屸埓a+b=-1锛屸埓鍘熷紡=2014-1=2013锛庢晠閫塀锛
绛旓細鈭祄銆乶鏄鏂圭▼x2+x-2012=0鐨勪袱涓疄鏁版牴锛屸埓m+n=-1锛屽苟涓攎2+m-2012=0锛屸埓m2+m=2011锛屸埓m2+2m+n=m2+m+m+n=2012-1=2011锛庢晠閫塂锛
绛旓細a²-2012a+1=0 鈭碼²=2012a-1 鍘熷紡=2012a-1-2011a+2012/(2012a-1+1)=a-1+1/a =(a²+1)/a-1 =(2012a-1+1)/a-1 =2012-1 =2011
绛旓細鑻鏂圭▼x²-2011x-2012=0鍜寈²锛201x-2012=0鐨勮緝灏忔牴鍒嗗埆涓篴鍜b锛鍒檃b鐨勫间负锛 C.2012 锛
绛旓細鈭 x1^2-x1-2015=0銆亁1+x2=1 鎵浠 x1^3+2016x2-201=x1(x1+2015)+2016x2-201 =x1^2+2015x1+2016x2-201 =x1+2015+2015x1+2016x2-201 =2016(x1+x2)+2015-201 =4031-201 =3830 銆愯嫢201鏄2015涔嬭锛屽垯=2016 锛涜嫢201鏄2016涔嬭 锛屽垯 =2015銆
绛旓細闊﹁揪瀹氱悊m+n=2011-m-n=-2011mn=-2012-m*锛-n锛=-2012鎵浠-m鍜-n鏄柟绋锛x²+2011x-2012=0鐨2涓牴閭d箞浠e叆(-m)²+2011m-2012=0m²+2011m=2012鍚岀悊n²+2011n=2012浠f暟寮=(2012-2011)/(2012-2013)=1/(-1)=-1 ...
绛旓細瑙:璁惧叏绋嬩负1,鐢茬殑閫熷害涓x涔欑殑閫熷害涓簓 鍒楀紡40x+40y=1 x:y=5:4 寰梮=1/72 y=1/90 璧板畬鍏ㄧ▼鐢查渶72鍒嗛挓,涔欓渶90鍒嗛挓 鏁呭緱瑙 9.鐢蹭箼涓よ溅鍚屾椂浠AB涓ゅ湴鐩稿寮鍑恒傜涓娆$浉閬囧悗涓よ溅缁х画琛岄┒,鍚勮嚜鍒拌揪瀵规柟鍑哄彂鐐瑰悗绔嬪嵆杩斿洖銆傜浜屾鐩搁亣鏃剁B鍦扮殑璺濈鏄AB鍏ㄧ▼鐨1/5銆傚凡鐭ョ敳杞﹀湪绗竴娆$浉閬囨椂琛屼簡120...