已知x^2+2y^2=1.求2x+5y^2的最小值

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已知x^2+2y^2=1.求2x+5y^2的最小值
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已知x^2+2y^2=1.求2x+5y^2的最小值
已知x^2+2y^2=1.求2x+5y^2的最小值

已知x^2+2y^2=1.求2x+5y^2的最小值
x^2+2y^2=1
|x|<=1
y^2=(1-x^2)/2
2x+5y^2
=2x+(1-x^2)(5/2)
=-(5/2)x^2+2x+(5/2)=f(x)
|x|<=1
f(-1)=min=-2

x^2+2y^2=1
x^2>=0 y>=0
x^2=1-2y^2>=0
0<=y^2<=1
2x+5y^2=2(x^2+2y^2)+y^2=2+y^2
最小值为2