平方差公式计算题五十道平方差公式计算题20道
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1、1. 8ab解法：(a+2b)^2=(a-2b)^2+na^2+4ab+4b^2=a^2-4ab+b^2+n 8ab =n 2.7解法：（a+1/a）^2=3^2 a^2+1/a^2+2=9 a^2+1/a^2 =7 3.(x^6+8)/(x^2+2)(x^2+2)n=x^6+8 n=(x^6+8)/(x^2+2) 4.x^4-6x^2y^2+4y^4(x-2y)(x-y)(x^2+3xy+2y^2) =.(x-2y)(x-y)(x+2y)(x+y) = (x-2y)(x+2y)(x-y)(x+y) =(x^2-4y^2)(x^2-y^2) =x^4-6x^2y^2+4y^4 5.x=-2(3x-2)^2-(3x+2)^2=48 9x^2-12x+4-9x^2-12x-4=48 -24x =48 x =-2 6.x=2,y=43x^2+4xy+y^2-4x+4=0 (y^2+4xy+4x^2)-x^2-4x+4=0 (y-2x)^2-(2-x)^2=0 x=2 y=47. (x+y)^2-(x+y)(x-y) =4 已知：.x^2+xy=7,……1 y^2+xy=2……2 1+2。
2、得 x^2+y^2+2xy=9 (x+y)^2 =91-2,得 x^2+xy-y^2-xy=7-2 x^2-y^2=5&。
绛旓細渚嬶細杩愮敤鍏紡璁＄畻(4a-3b+c)(4a+3b+c)瑙ｏ細(4a-3b+c)(4a+3b+c)锛漑(4a+c)-3b][(4a+c)+3b]锛(4a+c)2-(3b)2 锛16a2+8ac+c2-9b2锛庢湰棰樻槸骞虫柟宸叕寮涓庡畬鍏骞虫柟鍏紡缁煎悎杩愮敤鐨璁＄畻棰锛庡厛杩愮敤骞虫柟宸叕寮忎氦鎹㈡垚鍚岄」鍦ㄥ墠鐩稿弽椤瑰湪鍚庝负(4a+c-3b)(4a+c+3b)锛庡啀鐢ㄥ钩鏂瑰樊鍏紡涓殑a...
绛旓細10鐨骞虫柟-9鐨勫钩鏂+8鐨勫钩鏂-7鐨勫钩鏂+6鐨勫钩鏂-5鐨勫钩鏂+4鐨勫钩鏂-3鐨勫钩鏂+2鐨勫钩鏂-1鐨勫钩鏂 =(10+9)(10-9)+(8+7)(8-7)+...(2+1)(2-1)=10+9+8+...+2+1 =55
绛旓細a^2-b^2= (2a+3b)(2a-3b)= c^4-d^4= (a^2-b^2)/(a-b)= ( 鈭3+ 鈭2)( 鈭3- 鈭2)= 3-2= ( 鈭歛+ 鈭歜)( 鈭歛- 鈭歜)= 鑻>0,b>0.a-b=
绛旓細锛2+1锛夛紙2^2+1锛夛紙2^4+1锛夛紙2^8+1锛夛紙2^16+1锛+1 =锛2-1锛夛紙2+1锛夛紙2^2+1锛夛紙2^4+1锛夛紙2^8+1锛夛紙2^16+1锛+1 =锛2^2-1锛夛紙2^2+1锛夛紙2^4+1锛夛紙2^8+1锛夛紙2^16+1锛+1 =锛2^4-1锛夛紙2^4+1锛夛紙2^8+1锛夛紙2^16+1锛+1 鈥︹ =锛2^16-1)(2^16+1...
绛旓細=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4锛(1-1/5)(1+1/5)=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)(4/5)(6/5)=(1/2)(6/5)=6/10 =3/5
绛旓細璁剧埛鐖蜂负X宀,濂跺ザ涓篩宀乆骞虫柟-Y骞虫柟=133鍙湁1*133=133鎴7*19=133涓ょ鎯呭喌X+Y=133,X-Y=1 ,X=67,Y=66X+Y=19,X-Y=7 ,X=13,Y=6鐖风埛鍜屽ザ濂跺勾榫勫ぇ,鎵浠ョ埛鐖67,濂跺ザ66鐜嬪崕鍜屾潕鏄庡勾绾皬,鎵浠ユ潕鏄13,鐜嬪崕6
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绛旓細鍒嗚В鍥犲紡锛4y^ 2-9x^ 2=(2y+3x)(2y-3x) x^ 2-1=(x+1)(x-1) a^ 2-b^ 4=(a+b^ 2)(a-b^ 2) x^ 4-16=( x^ 2+4)( x^ 2 -4)=( x^ 2+4)( x+2)(x-2)
绛旓細鍗曚釜鍋忕鏄秷闄ょ鍙峰奖鍝嶆柟宸嵆鍋忕骞虫柟鐨勫潎鍊硷紝璁颁负D(X )锛氱洿鎺璁＄畻鍏紡鍒嗙鏁ｅ瀷鍜岃繛缁瀷锛屽叿浣撲负锛氳繖閲 鏄竴涓暟銆傛帹瀵煎彟涓绉嶈绠楀叕寮 寰楀埌锛氣滄柟宸瓑浜庡钩鏂圭殑鍧囧煎噺鍘诲潎鍊肩殑骞虫柟鈥濄傚叾涓紝鍒嗗埆涓虹鏁ｅ瀷鍜岃繛缁瀷鐨勮绠楀叕寮忋 绉颁负鏍囧噯宸垨鍧囨柟宸紝鏂瑰樊鎻忚堪娉㈠姩 骞虫柟宸叕寮锛氫袱涓暟鐨勫拰涓庤繖涓や釜鏁扮殑...
绛旓細100^2-99^2+98^2-97^2+96^2-95^2+...+2^2-1^2 =(100+99)(100-99)+(98+97)(98-97)+鈥︹︹+(2+1)(2-1)=100+99+98+97+鈥︹︹+3+2+1=5050 1992^2-1993涔1991= =1992脳1992-锛1992+1锛夛紙1992-1锛=1992脳1992-锛1992脳1992-1脳1锛=1 ...
