柯西不等式解方程组x+y+z=9,x+w=6,(x^2+y^2+z^2)(x^2+w^2)=486
解方程组x+y+z=9,x+w=6,(x^2+y^2+z^2)(x^2+w^2)=486
推荐回答（2个）
x = y = z = w = 3.
考的就是柯西不等式的配凑~
根据柯西不等式：
(x^2+y^2+z^2)(1^2+1^2+1^2)
>= (x+y+z)^2.
(x^2+w^2)(1^2+1^2)
>= (x+w)^2
所以
(x^2+y^2+z^2)*3*(x^2+w^2)*2
>= (x+y+z)^2 * (x+w)^2
= 9^2 * 6^2
所以
(x^2+y^2+z^2)(x^2+w^2) >= 486
取得等号，当且仅当 x = y =z =w
因此，x = y = z = w = 3。
meet you in this life is my greatest happiness
miss the edge of
in the wind are my every tear
sound of the sighing
night without you
loneliness is my
Dream of Rao's thoughts
If you can not hear the wind call your voice I let this affectionate
forever in my heart
accompanied me every day
night without you in the sky no more tears
because I had flown
lifetime devotion
is not also looking forward to an eternal life of pain
not look forward to a memory
life is not also miss
looking forward to a kind of Acacia
even only be a continuation of
sad this life you and I are doomed to separation
ah ah ah
life longing
lyrics: Ho Cheng
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