(x^2)+(y^2)+(z^2)
= x^2 + 1/2y^2 + 1/2y^2 + z^2
≥ 2√(1/2)xy + 2√(1/2)yz
=√2 (xy+yz)
所以(xy+yz)/[(x^2)+(y^2)+(z^2)] ≤ √2/2
最大值為√2/2
當(dāng)√2x = y = √2z時(shí)取得
(注：這里x,y,z應(yīng)該是正數(shù),而不是正整數(shù),否則無(wú)法取得最大值√2/2,但可以無(wú)限接近)