【就一部不懂】如果x、y∈R,且x≠y,比较(x2+y2)2与xy(x+y)2大小作差法 (x2+y2)2-xy(x+y)2 =x^4+y^4+2x^2y^2-x^3y-2x^2y^2-xy^3 =(x-y)(x^3-y^3) =(x-y)^2[(x+y/2)^2+3y^2/4] ∵x≠y (x-y)^2>0,(x+y/2)^2+3y
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![【就一部不懂】如果x、y∈R,且x≠y,比较(x2+y2)2与xy(x+y)2大小作差法 (x2+y2)2-xy(x+y)2 =x^4+y^4+2x^2y^2-x^3y-2x^2y^2-xy^3 =(x-y)(x^3-y^3) =(x-y)^2[(x+y/2)^2+3y^2/4] ∵x≠y (x-y)^2>0,(x+y/2)^2+3y](/uploads/image/z/8639412-60-2.jpg?t=%E3%80%90%E5%B0%B1%E4%B8%80%E9%83%A8%E4%B8%8D%E6%87%82%E3%80%91%E5%A6%82%E6%9E%9Cx%E3%80%81y%E2%88%88R%2C%E4%B8%94x%E2%89%A0y%2C%E6%AF%94%E8%BE%83%28x2%2By2%292%E4%B8%8Exy%28x%2By%292%E5%A4%A7%E5%B0%8F%E4%BD%9C%E5%B7%AE%E6%B3%95+%28x2%2By2%292-xy%28x%2By%292+%3Dx%EF%BC%BE4%2By%EF%BC%BE4%2B2x%EF%BC%BE2y%EF%BC%BE2-x%EF%BC%BE3y-2x%EF%BC%BE2y%EF%BC%BE2%EF%BC%8Dxy%EF%BC%BE3+%3D%28x-y%29%28x%EF%BC%BE3-y%EF%BC%BE3%29+%3D%28x-y%29%EF%BC%BE2%5B%28x%2By%2F2%29%EF%BC%BE2%2B3y%EF%BC%BE2%2F4%5D+%E2%88%B5x%E2%89%A0y+%28x-y%29%EF%BC%BE2%EF%BC%9E0%2C%28x%2By%2F2%29%EF%BC%BE2%2B3y)
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【就一部不懂】如果x、y∈R,且x≠y,比较(x2+y2)2与xy(x+y)2大小作差法 (x2+y2)2-xy(x+y)2 =x^4+y^4+2x^2y^2-x^3y-2x^2y^2-xy^3 =(x-y)(x^3-y^3) =(x-y)^2[(x+y/2)^2+3y^2/4] ∵x≠y (x-y)^2>0,(x+y/2)^2+3y
【就一部不懂】如果x、y∈R,且x≠y,比较(x2+y2)2与xy(x+y)2大小
作差法
(x2+y2)2-xy(x+y)2
=x^4+y^4+2x^2y^2-x^3y-2x^2y^2-xy^3
=(x-y)(x^3-y^3)
=(x-y)^2[(x+y/2)^2+3y^2/4]
∵x≠y
(x-y)^2>0,(x+y/2)^2+3y^2/4>0
∴(x2+y2)2>xy(x+y)2
=(x-y)^2[(x+y/2)^2+3y^2/4] 这部是怎么做出来的?
【就一部不懂】如果x、y∈R,且x≠y,比较(x2+y2)2与xy(x+y)2大小作差法 (x2+y2)2-xy(x+y)2 =x^4+y^4+2x^2y^2-x^3y-2x^2y^2-xy^3 =(x-y)(x^3-y^3) =(x-y)^2[(x+y/2)^2+3y^2/4] ∵x≠y (x-y)^2>0,(x+y/2)^2+3y
因为
a^3-b^3=(a-b)(a^2+ab+b^2)= (a-b)[a^2+ab+b^2/4+b^2(3/4)]
=(a-b)[(a+b/2)^2+3b^2/4]
【就一部不懂】如果x、y∈R,且x≠y,比较(x2+y2)2与xy(x+y)2大小作差法 (x2+y2)2-xy(x+y)2 =x^4+y^4+2x^2y^2-x^3y-2x^2y^2-xy^3 =(x-y)(x^3-y^3) =(x-y)^2[(x+y/2)^2+3y^2/4] ∵x≠y (x-y)^2>0,(x+y/2)^2+3y
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