已知实数x,y满足x²+y²+2x+2√3y=0.求x²+y²的最大值.②求x+y的最小值.最好是带讲解!
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已知实数x,y满足x²+y²+2x+2√3y=0.求x²+y²的最大值.②求x+y的最小值.最好是带讲解!
已知实数x,y满足x²+y²+2x+2√3y=0.求x²+y²的最大值.②求x+y的最小值.最好是带讲解!
已知实数x,y满足x²+y²+2x+2√3y=0.求x²+y²的最大值.②求x+y的最小值.最好是带讲解!
x²+y²+2x+2√3y=0
→(x+1)²+(y+√3)²=2².
故可设x+1=2cosα,y+√3=2sinα.
于是:
(1)x²+y²
=(-1+2cosα)²+(-√3+2sinα)²
=8-8[sinα·(√3/2)+cosα·(1/2)]
=8-8sin(α+π/6).
∵sin(α+π/6)∈[-1,1],
∴sin(α+π/6)=1时,(x²+y²)|min=0;
sin(α+π/6)=-1时,(x²+y²)|max=16.
(2)x+y
=(-1+2cosα)+(-√3+2sinα)
=-1-√3+2√2sin(α+π/4).
∵sin(α+π/4)∈[-1,1],
∴sin(α+π/4)=1时,(x+y)|max=-1-√3+2√2;
sin(α+π/4)=-1时,(x+y)|min=-1-√3-2√2.
x²+y²+2x+2√3y=0
(x+1)²+(y+√3)²=2^2与x²+y²=a^2,表示圆与圆关系求
(x+1)²+(y+√3)²=2^2与x+y=b表示圆与直线关系