s[y^2*(y-z)*(y*(x-z)^2+2*x*z*(x-3*z))]>=0、s[x*y*(x+y)*(y-z)*(x*(y-z)^2-2*z^2*(5*x-z))]>=0、s[x*y*(x*y+z^2)*(y-z)*((x+5*y)*(x+2*z)-20*y*z)]>=0、s[x^2*y*(x+z)*(y-z)*((y+z)*(3*x+7*y+9*z)-22*y*z)]>=0、s[x*(x^2*y-4*x*y^2+x*y*z-x*z^2+2*y^2*z+y*z^2)*(x^3*y-3*x^2*y^2+2*x^2*y*z-5*x^2*z^2+x*y^2*z+3*x*y*z^2-x*z^3-y^2*z^2+3*y*z^3)]≥0、……
不等式吧 关注：9,834贴子：51,935
- 1回复贴，共1页
s(b2(b-c)(b(a-c)2+2ac(a-3c))) * s(a^2c-abc)
=s(c(a-c)^2(2b^2a-b^2c-ba^2-bac+a^2c)^2)
——
s(ab(a+b)(b-c)(a(b-c)2-2c2(5a-c))) * s(a)
=1/2s((-a^2bc+a^2c^2+ab^3-2ab^2c+3abc^2-b^2c^2-bc^3)^2)+s(ac(a^2c-3ab^2+abc+2b^2c-bc^2)^2)
——
s(ab(ab+c2)(b-c)((a+5b)(a+2c)-20bc)) * s(2522ab^2+1610ac^2+2019a(a-b)(a-c))
=1/2s((9334a^4+14111a^3c+4038ac^3+4038bc(-a+c)^2+3046(-a+c)^2(a-b)^2)(ab^2-abc-ac^2-b^2c+2bc^2)^2)+1/2s(ac^3(415a^2+100ac+572bc)(a^2-2ab-3ac-b^2+5bc)^2)+3623/2s(ab^3(-a^2c+ab^2+abc+2ac^2-3bc^2)^2)
——
s(a2b(a+c)(b-c)((b+c)(3a+7b+9c)-22bc)) * s(a)
=1/4s(a(3b+c)(a^2c-3ab^2+abc+2b^2c-bc^2)^2)+s(a(5a+3c)(ab^2-abc-ac^2-b^2c+2bc^2)^2)
——
s(a(a2b-4ab2+abc-ac2+2b2c+bc2)(a3b-3a2b2+2a2bc-5a2c2+ab2c+3abc2-ac3-b2c2+3bc3))
=1/12s((-a^2b^2+4a^2bc-6a^2c^2+5ab^2c-abc^2+2ac^3-3b^2c^2)^2)+1/96s((16a^2b^2-26a^2bc-a^2c^2-ab^2c+11abc^2-ac^3-3b^3c+5b^2c^2)^2)+1/4320s((19a^3b-129a^2b^2+75a^2bc+29a^2c^2+90ab^2c-85abc^2+ac^3)^2)+11/207s((5ab^2c-9abc^2+ac^3-2b^3c+5b^2c^2)^2)+11/49680s((69a^2c^2-145ab^2c-15abc^2-29ac^3-11b^3c+131b^2c^2)^2)
=s(c(a-c)^2(2b^2a-b^2c-ba^2-bac+a^2c)^2)
——
s(ab(a+b)(b-c)(a(b-c)2-2c2(5a-c))) * s(a)
=1/2s((-a^2bc+a^2c^2+ab^3-2ab^2c+3abc^2-b^2c^2-bc^3)^2)+s(ac(a^2c-3ab^2+abc+2b^2c-bc^2)^2)
——
s(ab(ab+c2)(b-c)((a+5b)(a+2c)-20bc)) * s(2522ab^2+1610ac^2+2019a(a-b)(a-c))
=1/2s((9334a^4+14111a^3c+4038ac^3+4038bc(-a+c)^2+3046(-a+c)^2(a-b)^2)(ab^2-abc-ac^2-b^2c+2bc^2)^2)+1/2s(ac^3(415a^2+100ac+572bc)(a^2-2ab-3ac-b^2+5bc)^2)+3623/2s(ab^3(-a^2c+ab^2+abc+2ac^2-3bc^2)^2)
——
s(a2b(a+c)(b-c)((b+c)(3a+7b+9c)-22bc)) * s(a)
=1/4s(a(3b+c)(a^2c-3ab^2+abc+2b^2c-bc^2)^2)+s(a(5a+3c)(ab^2-abc-ac^2-b^2c+2bc^2)^2)
——
s(a(a2b-4ab2+abc-ac2+2b2c+bc2)(a3b-3a2b2+2a2bc-5a2c2+ab2c+3abc2-ac3-b2c2+3bc3))
=1/12s((-a^2b^2+4a^2bc-6a^2c^2+5ab^2c-abc^2+2ac^3-3b^2c^2)^2)+1/96s((16a^2b^2-26a^2bc-a^2c^2-ab^2c+11abc^2-ac^3-3b^3c+5b^2c^2)^2)+1/4320s((19a^3b-129a^2b^2+75a^2bc+29a^2c^2+90ab^2c-85abc^2+ac^3)^2)+11/207s((5ab^2c-9abc^2+ac^3-2b^3c+5b^2c^2)^2)+11/49680s((69a^2c^2-145ab^2c-15abc^2-29ac^3-11b^3c+131b^2c^2)^2)
