已知实数X,y满足(X-2)²+y²=3,求|x一y十4|的最值.
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已知实数X,y满足(X-2)²+y²=3,求|x一y十4|的最值.
已知实数X,y满足(X-2)²+y²=3,求|x一y十4|的最值.
已知实数X,y满足(X-2)²+y²=3,求|x一y十4|的最值.
利用三角代换
∵(x-2)²+y²=3
令x=2+√3cosΘ,y=√3sinΘ
则x-y+4
=2+√3cosΘ-√3sinΘ+4
=√6*[cosΘ*(√2/2)-sinΘ*(√2/2)]+6
=√6*[cosΘ*cos(π/4)-sinΘ*sin(π/4)]+6
=√6cos(Θ+π/4)+6>0(因为-1≤cos(Θ+π/4)≤1)
∴|x-y+4|=√6cos(Θ+π/4)+6
∴最大值是√6+6,最小值是-√6+6.
利用三角代换
∵(x-2)²+y²=3
令x=2+√3cosΘ,y=√3sinΘ
则x-y+4
=2+√3cosΘ-√3sinΘ+4
=√6*[cosΘ*(√2/2)-sinΘ*(√2/2)]+6
=√6*[cosΘ*cos(π/4)-sinΘ*sin(π/4)]+6
=√6cos(Θ+π/4)+6>0(因为-1...
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利用三角代换
∵(x-2)²+y²=3
令x=2+√3cosΘ,y=√3sinΘ
则x-y+4
=2+√3cosΘ-√3sinΘ+4
=√6*[cosΘ*(√2/2)-sinΘ*(√2/2)]+6
=√6*[cosΘ*cos(π/4)-sinΘ*sin(π/4)]+6
=√6cos(Θ+π/4)+6>0(因为-1≤cos(Θ+π/4)≤1)
∴|x-y+4|=√6cos(Θ+π/4)+6
∴最大值是√6+6,最小值是-√6+6。
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