x方加y方的平方小于等于4x方减y方

投稿:花尽千霜默 优质问答领域创作者 发布时间:2023-10-05 23:19:46
x方加y方的平方小于等于4x方减y方

最小值f(x,y)|min=-4,此时,x=0,y=2。以上x、y值都满足x²+y²≤4。

(x²+y²)²-4x²y²

=(x²+y²)²-(2xy)²

=[(x²+y²)-2xy][(x²+y²)+2xy]

=(x²+y²-2xy)(x²+y²+2xy)

=[x²-2(x)(y)+y²][x²+2(x)(y)+y²]

=(x-y)²(x+y)²

x方加y方的平方小于等于4x方减y方

(x方+y方)的平方-4x方y方 =[(x^2+y^2)+2xy][(x^2+y^2)-2xy] =(x+y)^2(x-y)^2