a的4次方-b的4次方
(a+b)\u76843\u6b21\u65b9\u30014\u6b21\u65b9\u600e\u4e48\u7b97\uff1f(a+b)^3
=(a+b)(a+b)^2
=(a+b)(a^2+2ab+b^2)
=a^3+b^3+3ab^2+3a^2b
(a+b)^4
=(a+b)^2(a+b)^2
=(a^2+2ab+b^2)(a^2+2ab+b^2)
=a^4+4a^3b+6a^2b^2+4ab^3+b^4
\u539f\u5148\u4e0a\u9762\u7684\u201c\u7cbe\u5f69\u56de\u7b54\u201c\u662f\u9519\u7684\uff01
a^4-b^4
=(a^2-b^2)(a^2+b^2)
=(a-b)(a+b)(a^2+b^2)
绛旓細a^4-b^4=(a^2+b^2)(a+b)(a-b)
绛旓細鍘熷紡=x^4-a²x²-b²x²+a²b²=x²(x²-a²)-b²(x²-a²)=(x²-b²)(x²-a²)=(x+b)(x-b)(x+a)(x-a)
绛旓細a^4-b^4=1+2b²a^4-b^4-2b²-1=0 a^4-(b²+1)²=0 (a²-b²-1)(a²+b²+1)=0
绛旓細瀹炴暟鑼冨洿涓細(a^2+b^2)(a+b)(a-b)澶嶆暟鑼冨洿涓細(a+b)(a-b)(a+bi)(a-bi)
绛旓細锛a鐨4娆℃柟-b鐨4娆℃柟锛夐櫎浠ワ紙a鐨勫钩鏂+b鐨勫钩鏂癸級闄や互锛坅-b锛=(a²+b²)(a+b)(a-b)/[(a²+b²)(a-b)]=a+b
绛旓細(a^4-b^4)/(a^2+b^2)/(a+b)鍘熷紡=(a^4-b^4)/(a^2+b^2)*(1/(a+b))=((a^2+b^2)(a^2-b^2))/(a^2+b^2)*(1/(a+b))=(a^2-b^2)*(1/(a+b))=(a^2-b^2)/(a+b)=((a+b)(a-b))/(a+b)=a-b 鎵浠ュ師寮忕瓑浜 a-b銆
绛旓細(a鐨4娆℃柟-b鐨4娆℃柟)梅(a鐨勫钩鏂+b鐨勫钩鏂)梅(a+b)=(a鐨勫钩鏂+b鐨勫钩鏂)(a鐨勫钩鏂-b鐨勫钩鏂)梅(a鐨勫钩鏂+b鐨勫钩鏂)梅(a+b)=(a鐨勫钩鏂-b鐨勫钩鏂)梅(a+b)=(a+b)(a-b)梅(a+b)=a-b
绛旓細鏍瑰彿(a骞虫柟-b骞虫柟)(a鐨4娆℃柟-b鐨4娆℃柟)=鈭氾紙a²-b²锛(a²-b²)(a²+b²)=|a²-b²|鈭(a²+b²);濡傛灉鏈鏈変粈涔堜笉鏄庣櫧鍙互杩介棶锛屽鏋滄弧鎰忚寰楅噰绾 濡傛灉鏈夊叾浠栭棶棰樿閲囩撼鏈鍚庡彟鍙戠偣鍑诲悜鎴戞眰鍔╋紝绛旈涓嶆槗锛岃璋呰В锛岃阿璋傜...
绛旓細璇﹁В瑙佸浘
绛旓細瑙ｏ細a鐨勫洓娆℃柟鍑81b鐨勫洓娆℃柟 =锛坅²+9b²锛夛紙a²-9b²锛=锛坅²+9b²锛夛紙a+3b锛夛紙a-3b锛夋墍鐢ㄥ叕寮忥細a²-b²=锛坅+b锛夛紙a-b锛変笉浼氳繕鍙互鍐嶉棶鎴戯紝甯屾湜閲囩撼锛孫(鈭鈭)O璋㈣阿!
