X平方加Y平方加Z平方等于110的正整数解有多少组?
平方数有0,1,4,9,16,25,36,49,64,81,100用枚举法
当1+9+100=110
可以是1,3,10
当81+4+25=110
所以可以是2,5,9
当25+16+49=110
所以可以是4,5,7
绛旓細x²+锛y-1)²+锛z-1锛²=1 x²+y²+z²-2y-2z+2=1 1-2(y+z)+2=1 y+z=1
绛旓細2x+y+z=11 x+2y+z=16 x+y+2z=17 宸﹁竟鍔犲乏杈癸紝鍙宠竟鐩稿姞 寰楀嚭3x+3y+3z=44 闄3 x+y+z=44/3 鍐嶄緷娆$敤涓婇潰鐨勫紡瀛愬噺鍘讳笅闈㈠緱鍑虹殑寮忓瓙 寰楀嚭x=-11/3 y=4/3 z=7/3
绛旓細璇烽噰绾
绛旓細瑙f湁鏃犻檺缁 鏁存暟瑙f湁鏃犻檺缁 姝f暣鏁拌В鏈9+8+7+6+5+4+3+2+1锛45缁 鑻ュ彲浠ョ瓑0锛屽垯鏈12+11+10+9+8+7+6+5+4+3+2+1=78缁
绛旓細x+y+z=11 y=2z 3x+y=19 閭d箞鐢变簬y=2z 鎵浠+y+z=x+2z+z=11 鎵浠+3z=11 涓3x+y=3x+2z=19 閭d箞灏卞緱鍑轰竴涓2鍏冧竴娆℃柟绋嬬粍 x+3z=11 3x+2z=19 瑙e緱x=5,z=2 閭d箞鐢眣=2z=2*2=4 鎵浠=5,y=4 z=2
绛旓細2x+y+z=0 锛1锛4x+5y+3z=0 锛2锛夌敱锛1锛夊緱 4x+2y+2z=0 锛3锛夛紙2锛夊噺锛3锛夊緱 3y+z=0 锛4锛夋墍浠=-3y 浠e叆锛1锛夊緱 2x-2y=0 鎵浠x=y 浠e叆x^2+y^2+z^2=1 寰 y^2+y^2+9y^2=1 鎵浠11y^2=1 鎵浠= (鈭11)/11 鎴杫=-(鈭11)/11 鎵浠=y = (鈭11)/11 鎴杧...
绛旓細鏇茬嚎x^2+y^2=3 y=1缁z杞存棆杞竴鍛ㄦ墍褰㈡垚鐨勬棆杞綋鏇查潰鏂圭▼涓 杩欐槸鏃嬭浆鏇查潰 f锛坹,z锛=0 鎵浠ユ棆杞洸闈㈡槸f锛+-鈭氾紙x^2+y^2锛,z锛=0 鎵浠ユ洸闈鏄痻^2+y^2=(z^2+1)^2
绛旓細鍥
绛旓細浠 f(x锛y锛寊)= x^2 + 2y^2 + 3z^2 - 11锛屽垎鍒眰鍏充簬 x銆亂銆z 鐨鍋忓鏁帮紝寰 2x銆4y銆6z锛屽洜涓哄垏骞抽潰涓 x+y+z = 1 骞宠锛屾墍浠 2x锛4y锛6z = 1锛1锛1锛岀粨鍚堟洸闈㈡柟绋嬶紝鍙В寰楀垏鐐癸紙鈭6锛屸垰6/2锛屸垰6/3锛夋垨锛-鈭6锛-鈭6/2锛-鈭6/3锛夛紝鎵浠ュ垏骞抽潰鏂圭▼涓 x+y+z = ...
绛旓細x^2+y^2+z^2+4x+4y+4z+1=0鏁寸悊寰楀埌锛(x+2)²+锛坹+2)²+(z+2)²=11;瑕佷娇鍏骞虫柟鍜屼负11锛屽垯鏁版嵁鍒嗗埆涓-5銆-1銆-1鎴栧垯1銆-1銆-1銆傛墍浠+y+z=-7鎴-1