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不等式吧 关注:10,029贴子:52,351
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简约而不简单的3元10次对称不等式

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  • 新世纪学者nice
  • 兰州烧饼
    10
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对任意实数x, y, z,有:4*s[(y*z)*((y+z)*(y+z-x)-4*y*z)^2*((x-y)*(x-z))^2]-s[x*(y+z-x)]^2*p[(x-y)*(x-z)]>=0.
当x, y, z ≥ 0时,进一步有:s[(y*z)*((y+z)*x-(y-z)^2)^2*((x-y)*(x-z))^2]+4*s[y*x*(y+z-x)*(x-y)*(x-z)]*s[z*x*(y+z-x)*(x-y)*(x-z)]>=0.
提示: 最好是不用pqr。


  • forever豪3
  • 虎躯一震
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loydman发了啥


2025-07-30 08:28:06
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  • Loydman
  • 鸭梨山大
    11
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140/11 (x^2 y^2 z^2-x^2 y z^3-x y^2 z^3+x y z^4)^2+(x^5 y-x^4 y^2-x^3 y^3+x^2 y^4-x^5 z-2 x^3 y^2 z-x y^4 z+x^4 z^2+2 x^3 y z^2+5 x y^3 z^2+x^3 z^3-5 x y^2 z^3-x^2 z^4+x y z^4)^2+(x^4 y^2-x^3 y^3-x^2 y^4+x y^5-x^4 y z-2 x^2 y^3 z-y^5 z+5 x^3 y z^2+2 x y^3 z^2+y^4 z^2-5 x^2 y z^3+y^3 z^3+x y z^4-y^2 z^4)^2+4/561 (66 x^3 y^2 z-77 x^2 y^3 z+11 x y^4 z+8 x^4 z^2-42 x^3 y z^2+14 x^2 y^2 z^2+31 x y^3 z^2-8 y^4 z^2-8 x^3 z^3+15 x^2 y z^3-21 x y^2 z^3+8 y^3 z^3-8 x^2 z^4+3 x y z^4+8 y^2 z^4+8 x z^5-8 y z^5)^2+5/11 (x^4 z^2+3 x^3 y z^2-3 x y^3 z^2-y^4 z^2-x^3 z^3-6 x^2 y z^3+6 x y^2 z^3+y^3 z^3-x^2 z^4+y^2 z^4+x z^5-y z^5)^2+1/33 (22 x^2 y^3 z-22 x y^4 z-x^4 z^2-3 x^3 y z^2-28 x^2 y^2 z^2+25 x y^3 z^2+y^4 z^2+x^3 z^3+12 x^2 y z^3-y^3 z^3+x^2 z^4-6 x y z^4-y^2 z^4-x z^5+y z^5)^2+1/17 (17 x^4 y z-21 x^3 y^2 z-x^2 y^3 z+5 x y^4 z-x^4 z^2-16 x^3 y z^2+28 x^2 y^2 z^2-6 x y^3 z^2+y^4 z^2+x^3 z^3-4 x^2 y z^3-8 x y^2 z^3-y^3 z^3+x^2 z^4+6 x y z^4-y^2 z^4-x z^5+y z^5)^2
43/984 (-x^9 y^4+2 x^7 y^6-x^5 y^8+4 x^7 y^4 z^2-5 x^5 y^6 z^2+3 x^3 y^8 z^2+x^9 z^4-4 x^7 y^2 z^4-3 x^3 y^6 z^4-2 x^7 z^6+5 x^5 y^2 z^6+3 x^3 y^4 z^6+x^5 z^8-3 x^3 y^2 z^8)^2+43/984 (-x^8 y^5+2 x^6 y^7-x^4 y^9+3 x^8 y^3 z^2-5 x^6 y^5 z^2+4 x^4 y^7 z^2-3 x^6 y^3 z^4-4 x^2 y^7 z^4+y^9 z^4+3 x^4 y^3 z^6+5 x^2 y^5 z^6-2 y^7 z^6-3 x^2 y^3 z^8+y^5 z^8)^2+(75 x^9 y^3 z-218 x^7 y^5 z+211 x^5 y^7 z-68 x^3 y^9 z-47 x^9 y z^3+14 x^7 y^3 z^3+14 x^5 y^5 z^3-21 x^3 y^7 z^3+26 x y^9 z^3+120 x^7 y z^5-42 x^5 y^3 z^5+28 x^3 y^5 z^5-64 x y^7 z^5-99 x^5 y z^7+7 x^3 y^3 z^7+50 x y^5 z^7+26 x^3 y z^9-12 x y^3 z^9)^2/7200+(889 (2 x^9 y z^3+x^7 y^3 z^3-x^3 y^7 z^3-2 x y^9 z^3-7 x^7 y z^5-2 x^5 y^3 z^5+2 x^3 y^5 z^5+7 x y^7 z^5+8 x^5 y z^7-8 x y^5 z^7-3 x^3 y z^9+3 x y^3 z^9)^2)/13728+(7 (143 x^7 y^5 z-286 x^5 y^7 z+143 x^3 y^9 z-178 x^9 y z^3-89 x^7 y^3 z^3+286 x^5 y^5 z^3-54 x^3 y^7 z^3-251 x y^9 z^3+480 x^7 y z^5-108 x^5 y^3 z^5-178 x^3 y^5 z^5+664 x y^7 z^5-426 x^5 y z^7+143 x^3 y^3 z^7-575 x y^5 z^7+124 x^3 y z^9+162 x y^3 z^9)^2)/1029600+1/4096((128 x^10 y^2 z-272 x^8 y^4 z+42 x^6 y^6 z+220 x^4 y^8 z-118 x^2 y^10 z-490 x^8 y^2 z^3+865 x^6 y^4 z^3-848 x^4 y^6 z^3+485 x^2 y^8 z^3+108 x^8 z^5+503 x^6 y^2 z^5-46 x^4 y^4 z^5-466 x^2 y^6 z^5-135 y^8 z^5-216 x^6 z^7-372 x^4 y^2 z^7+354 x^2 y^4 z^7+270 y^6 z^7+108 x^4 z^9+15 x^2 y^2 z^9-135 y^4 z^9)^2)+43/984 (3 x^8 y^2 z^3-3 x^6 y^4 z^3+3 x^4 y^6 z^3-3 x^2 y^8 z^3-x^8 z^5-5 x^6 y^2 z^5+5 x^2 y^6 z^5+y^8 z^5+2 x^6 z^7+4 x^4 y^2 z^7-4 x^2 y^4 z^7-2 y^6 z^7-x^4 z^9+y^4 z^9)^2+(3 (82 x^6 y^6 z-164 x^4 y^8 z+82 x^2 y^10 z+142 x^8 y^2 z^3-347 x^6 y^4 z^3+224 x^4 y^6 z^3-183 x^2 y^8 z^3-20 x^8 z^5-141 x^6 y^2 z^5+410 x^4 y^4 z^5+182 x^2 y^6 z^5+61 y^8 z^5+40 x^6 z^7-84 x^4 y^2 z^7-326 x^2 y^4 z^7-122 y^6 z^7-20 x^4 z^9+123 x^2 y^2 z^9+61 y^4 z^9)^2)/808192+1/946176((1232 x^8 y^4 z-3202 x^6 y^6 z+2708 x^4 y^8 z-738 x^2 y^10 z-1278 x^8 y^2 z^3+1891 x^6 y^4 z^3-3248 x^4 y^6 z^3+1647 x^2 y^8 z^3+1412 x^8 z^5+37 x^6 y^2 z^5+3702 x^4 y^4 z^5-2870 x^2 y^6 z^5+683 y^8 z^5-2824 x^6 z^7-476 x^4 y^2 z^7+1702 x^2 y^4 z^7-1366 y^6 z^7+1412 x^4 z^9-1107 x^2 y^2 z^9+683 y^4 z^9)^2)+1/946176((1412 x^8 y^5-2824 x^6 y^7+1412 x^4 y^9-1278 x^8 y^3 z^2+37 x^6 y^5 z^2-476 x^4 y^7 z^2-1107 x^2 y^9 z^2+1232 x^8 y z^4+1891 x^6 y^3 z^4+3702 x^4 y^5 z^4+1702 x^2 y^7 z^4+683 y^9 z^4-3202 x^6 y z^6-3248 x^4 y^3 z^6-2870 x^2 y^5 z^6-1366 y^7 z^6+2708 x^4 y z^8+1647 x^2 y^3 z^8+683 y^5 z^8-738 x^2 y z^10)^2)+1/4096((108 x^8 y^5-216 x^6 y^7+108 x^4 y^9+128 x^10 y z^2-490 x^8 y^3 z^2+503 x^6 y^5 z^2-372 x^4 y^7 z^2+15 x^2 y^9 z^2-272 x^8 y z^4+865 x^6 y^3 z^4-46 x^4 y^5 z^4+354 x^2 y^7 z^4-135 y^9 z^4+42 x^6 y z^6-848 x^4 y^3 z^6-466 x^2 y^5 z^6+270 y^7 z^6+220 x^4 y z^8+485 x^2 y^3 z^8-135 y^5 z^8-118 x^2 y z^10)^2)+(3 (-20 x^8 y^5+40 x^6 y^7-20 x^4 y^9+142 x^8 y^3 z^2-141 x^6 y^5 z^2-84 x^4 y^7 z^2+123 x^2 y^9 z^2-347 x^6 y^3 z^4+410 x^4 y^5 z^4-326 x^2 y^7 z^4+61 y^9 z^4+82 x^6 y z^6+224 x^4 y^3 z^6+182 x^2 y^5 z^6-122 y^7 z^6-164 x^4 y z^8-183 x^2 y^3 z^8+61 y^5 z^8+82 x^2 y z^10)^2)/808192+1/946176((1412 x^9 y^4-2824 x^7 y^6+1412 x^5 y^8-1107 x^9 y^2 z^2-476 x^7 y^4 z^2+37 x^5 y^6 z^2-1278 x^3 y^8 z^2+683 x^9 z^4+1702 x^7 y^2 z^4+3702 x^5 y^4 z^4+1891 x^3 y^6 z^4+1232 x y^8 z^4-1366 x^7 z^6-2870 x^5 y^2 z^6-3248 x^3 y^4 z^6-3202 x y^6 z^6+683 x^5 z^8+1647 x^3 y^2 z^8+2708 x y^4 z^8-738 x y^2 z^10)^2)+1/4096((108 x^9 y^4-216 x^7 y^6+108 x^5 y^8+15 x^9 y^2 z^2-372 x^7 y^4 z^2+503 x^5 y^6 z^2-490 x^3 y^8 z^2+128 x y^10 z^2-135 x^9 z^4+354 x^7 y^2 z^4-46 x^5 y^4 z^4+865 x^3 y^6 z^4-272 x y^8 z^4+270 x^7 z^6-466 x^5 y^2 z^6-848 x^3 y^4 z^6+42 x y^6 z^6-135 x^5 z^8+485 x^3 y^2 z^8+220 x y^4 z^8-118 x y^2 z^10)^2)+(3 (-20 x^9 y^4+40 x^7 y^6-20 x^5 y^8+123 x^9 y^2 z^2-84 x^7 y^4 z^2-141 x^5 y^6 z^2+142 x^3 y^8 z^2+61 x^9 z^4-326 x^7 y^2 z^4+410 x^5 y^4 z^4-347 x^3 y^6 z^4-122 x^7 z^6+182 x^5 y^2 z^6+224 x^3 y^4 z^6+82 x y^6 z^6+61 x^5 z^8-183 x^3 y^2 z^8-164 x y^4 z^8+82 x y^2 z^10)^2)/808192


  • 新世纪学者nice
  • 兰州烧饼
    10
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2楼大揭秘:


  • 新世纪学者nice
  • 兰州烧饼
    10
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解密第4楼:


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