求证:若x、y、x为正整数,xy/z亦为整数,若x、y>z则xy/z为合数;若x,y<z则z为合数 设x,y和z为向量空间V中的向量,证明:若x+y=x+z,则...
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x2+y2+z2=0\u3002
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但是这也太难了
好像只能穷举
先回答第一个设问，x，y>z，事实上，xy为合数(x,y都≥2)，要想得到xy／z为整数，则z必须被xy约成1，即XY含有Z的素因子，结合X和Y大于Z，很容易得到约分后依然可以得到两个大于或等于2的数相乘，其结果为合数，得证(只算是思路)
第二个结论，不妨设z为素数，则z只有1和z两个因数，而x，y小于z，显然无法把z约成1，那么xy／z不为整数，矛盾，因此z为合数，证毕。
(这是初中小蓝本的一个说明吧，事实上都跟算数基本定理有关)
绛旓細鑻ユ灉X锛漎,涓嶆垚绔嬨鑻涓嶇瓑浜Y锛寈,y鏄鏁存暟,鎵浠ュ繀鏈塜>Y鎴朮<Y,鍗硏\y<1鎴杫\x銆1锛屾墍浠1+x\y<2 鍜1+y\x<2蹇呮湁涓涓垚绔嬨
绛旓細鍥犱负x+y+xy=34锛屾墍浠+y+xy+1=35 鎵浠(x+1)(y+1)=35=5脳7 鎵浠+1=5锛寉+1=7鎴杧+1=7锛寉+1=5 鎵浠+1+y+1=12锛屾晠x+y=10.
绛旓細鈭祒2+y2+4y-96=0锛屸埓x2+锛坹+2锛2=100锛屸埓y=100?x2-2锛岃x锛寉涓烘鏁存暟锛鈭磝鍙兘鍙1锝9涔嬮棿鐨勬暣鏁帮紝鈭村綋x=6锛寉=6锛涘綋x=8锛寉=4锛屸埓xy=36鎴32锛庢晠绛旀涓猴細32锛36锛
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绛旓細鈭x銆亂鏄鏁存暟锛鍙堚埖姝ｆ暣鏁扮殑骞虫柟鐨勪釜浣嶄笂鐨勬暟瀛楀彧鑳芥槸0锛1锛4锛5锛6锛9锛岀浉鍔犵殑缁撴灉涓綅涓7鐨勫彧鏈1鍜6锛屸埓鍋囪x鐨勪釜浣嶄负1鎴9锛屽垯y鐨勪釜浣嶄负4鎴6锛屸埓褰搙=29鏃锛寉=34锛庘埓x+y=29+34=63锛庢晠绛旀涓猴細63锛
绛旓細锛1锛夆埖4x+16y=1锛屸埓x+y=锛坸+y锛夛紙4x+16y锛=20+锛4yx+16xy锛夆墺20+24yx?16xy=36锛庡綋涓斾粎褰4x+16y锛14yx锛16xy锛鍗硏=12锛寉=24鏃朵笂寮忕瓑鍙锋垚绔嬶紱锛2锛夌敱蟻=4cos胃锛屽緱蟻2=4蟻cos胃锛屽嵆x2+y2-4x=0锛屸埓鍦哋1鐨勫渾蹇冨潗鏍囦负锛2锛0锛夛紟鐢毕=-4sin胃锛屽緱蟻2=-4蟻sin胃锛屽嵆...
绛旓細鑻,y鍧涓烘鏁存暟 鎵鏈夎В锛2x+3y=40 x=2锛泍=12 x=5锛泍=10 x=8锛泍=8 x=11锛泍=6 x=14锛泍=4 x=17锛泍=2
绛旓細绛:x-y=a+3 2x+y=5a 涓ゅ紡鐩稿姞寰:3x=6a+3 鎵浠:x=2a+1 浠ｅ叆绗竴寮忚В寰:y=a-2 鍥犱负1<=a<=4锛屽苟涓y鏄鏁存暟锛鎵浠:1<=y=a-2<=2 褰搚=1鏃讹紝a=3锛寈=7 褰搚=2鏃讹紝a=4锛寈=9 鎵浠:a=3鎴栬卆=4
