x，y，z是三个有理数，若x<y，x+y=0，且xyz>0. 1、试判断x，y，z的正负性; 2 x y z是三个有理数，若x ＜ y x+y=0，且xyz＞...
x,y,z\u662f\u4e09\u4e2a\u6709\u7406\u6570\uff0c\u82e5x<y,x+y=0\uff0c\u4e14xyz>0. (1)\u8bd5\u5224\u65adx\uff0cy\uff0cz\u7684\u6b63\u8d1f\u6027;1\uff09x\u4e3a\u8d1f\u6570 y\u4e3a\u6b63\u6570 z\u4e3a\u8d1f\u6570 \u8fc7\u7a0b\uff1a\u2235x+y=0 \u5373x=-y \u53c8x<y \u2234x\uff1c0\u4e3a\u8d1f\u6570 y\uff1e0\u4e3a\u6b63\u6570 \u2235xyz\uff1e0 \u5373-y\u00d7y\u00d7z\uff1e0 \u2234z\uff1c0\u4e3a\u8d1f\u6570
2)\u7b26\u53f7\u4e3a\u6b63\u53f7
\u8fc7\u7a0b:\u2235x\uff1c
0 ,y\uff1e0 ,z\uff1c0 .\u2234x+z\uff1c0,x-y\uff1c0.\u2234(x+z)(x-y)>0\u7b26\u53f7\u4e3a\u6b63
\u61c2\u4e86\u4e48\uff1f
\u5982\u679c\u8fd8\u6709\u95ee\u9898\u7684\u8bdd\u6b22\u8fce\u8ffd\u95ee
\u671b\u91c7\u7eb3\u8c22\u8c22~
2：因为x＜0 y＞0 所以x－y＜0 Z＜0 所以x＋Z＜0所以（x＋z）（x－y）＞0
绛旓細锛嬪彿 杩介棶锛 娌¤繃绋嬶紵锛燂紵 鍥炵瓟锛 鍥犱负x<y,涓攛+y=0鎵浠鍜寉浜掍负鐩稿弽鏁帮紝涓攛锛0锛寉锛0銆傚張鍥犱负xyz锛0鎵浠z锛0銆傚垯锛坸锛媦锛夛紙x锛峺锛夛紳锛 璐熸暟 锛嬭礋鏁帮級锛堣礋鏁帮紞姝ｆ暟锛夛紳璐熸暟涔樿礋鏁帮紳姝ｆ暟 琛ュ厖锛 姹傞噰绾
绛旓細(1)n鏄鏁 x=2/[(-1)^n-1]=2/(-1-1)=-1 x涓巠浜掍负鐩稿弽鏁 鎵浠=1 y涓巣浜掍负鍊掓暟 鎵浠=1 鎵浠=-1,y=1,z=1 (2)xy锛峺^2012锛嶏紙y-x锛塣2013 =-1*1-1^2012-(1+1)^2013=-2-2^2013
绛旓細鍒濇鍒ゆ柇锛 x涓鸿礋鏁 y涓烘鏁 x鐨勭粷瀵瑰间笌y鐨勭粷瀵瑰肩浉绛 z涓鸿礋鏁 杩欐牱婊¤冻鏉′欢锛歺灏忎簬y锛寈+y=0锛寈yz澶т簬0 鏍规嵁杩欐牱鐨勫墠鎻愶細x+z锛寈-y鍧囦负璐熸暟 鐝棬寮勬枾浜嗭細銆
绛旓細x<0 y>0 z<0
绛旓細瑙ｏ細锛1锛夊綋n涓哄鏁版椂 = = 鈭x涓y浜掍负鐩稿弽鏁 鈭磞=-x=1鈭祔涓z 涓哄掓暟 鈭 鈭 =-1 =1 z=1 褰搉涓哄伓鏁版椂 = =0鈭靛垎姣嶄笉鑳戒负闆 鈭翠笉鑳芥眰鍑簒銆亂銆亃杩涓変釜鏁锛2锛夊綋 =-1 =1 z=1鏃 = = 锛1锛変簰涓虹浉鍙嶆暟鐨勪袱涓暟鐩稿姞寰0锛屼箻绉负1鐨勪袱...
绛旓細鍥
绛旓細瑙ｏ細瑙ｅ叧浜巟,y鐨勪簩鍏冧竴娆℃柟绋嬬粍{3x+2y=5-z,x+y=2+z}.寰梮=1-3z,y=1+4z.鐢x,y,z鈮0寰0鈮3z鈮1.鏁卻=2x+y-z=3-3z.===>3z=3-s.鐢0鈮3z鈮1.===>0鈮3-s鈮1.===>2鈮鈮3.===>smax=3,smin=2.
绛旓細姝ｆ暟鐨勭粷瀵瑰兼槸瀹冩湰韬紝璐熸暟鐨勭粷瀵瑰兼槸瀹冪殑鐩稿弽鏁般涓変釜閮戒负姝ｆ暟鏃讹紝绛変簬1+1+1=3锛涗竴姝ｄ袱璐熸椂锛岀瓑浜-1銆
绛旓細鍙栫粷瀵瑰肩鍙凤紝鍒嗙被璁ㄨ锛氳В锛 褰搙>0,y>0,z>0鏃 鍘熷紡=4 褰x,y,z 涓湁涓涓垨涓や釜鏄>0 鎴<0 鏃 鍘熷紡=0 褰搙<0,y<0,z<0鏃 鍘熷紡=-4 鎵浠ワ紝鍘熷紡鐨勫间负锛 4鎴0鎴-4
绛旓細x銆亂銆亃涓変釜涓洪潪璐熸湁鐞嗘暟?3x+2y+z=5,x+y-z=2 閫氳繃鍓嶉潰涓や釜寮忓瓙鐢▁鏉ヨ〃绀簓,z灏辫薄瑙ｆ柟绋嬩竴鏍 2寮忕浉鍔犲緱:4x+3y=7 y=(7-4x)/3,z=(1-x)/3 鍥犱负x,y,z涓3涓闈炶礋鏈夌悊鏁,y=(7-4x)/3>=0 z=(1-x)/3>=0 x>=0 寰:0 ...
