已知实数x、y满足方程x²+y²-4x=0,则y/x+2的取值范围是。
\u65b9\u7a0bx²-4x+3a²-2=0\u5728\u533a\u95f4[-1,1]\u4e0a\u6709\u5b9e\u6839\uff0c\u5219\u5b9e\u6570a\u7684\u53d6\u503c\u8303\u56f4\u662fx^2-4x+3a^2-2=0
x^2-4x-2=-a^2
\u8bbef(x)=x^2-4x-2
\u5219f(x)\u662f\u5f00\u53e3\u5411\u4e0a\u3001\u5bf9\u79f0\u8f74\u4e3ax=2\u7684\u4e8c\u6b21\u51fd\u6570\uff0c\u5728\u533a\u95f4[-1\uff0c1]\u4e0a\u9012\u51cf\u3002
f(x)\u5728\u533a\u95f4[-1\uff0c1]\u4e0a\u7684\u6700\u5927\u503c\u662ff(-1)=3\u3001\u6700\u5c0f\u503c\u662ff(1)=-5\u3002
\u6240\u4ee5\uff0c-5<=-3a^2<=3
\u89e3\u5f97\uff1a-\u221a15/3<=a<=\u221a15/3
.
\u56e0\u4e3a\u662f\u5173\u4e8ex\u7684\u65b9\u7a0b\u6709\u5b9e\u6839\uff0c\u6ca1\u8bf4\u662f\u4e8c\u6b21\u65b9\u7a0b\u8fd8\u662f\u4e00\u6b21\u65b9\u7a0b\uff0c\u5206\u7c7b\u8ba8\u8bba
\u2460\u4e00\u6b21\u65b9\u7a0b\uff0c\u5373a=5\u65f6\uff0c\u65b9\u7a0b-4x-1=0 x=-1/4\u6709\u5b9e\u6839\uff0ca\u7684\u53d6\u503c\u8303\u56f4\u4e3aa=5
\u2461\u4e8c\u6b21\u65b9\u7a0b\uff0c\u5373a\u22605\u65f6\uff0c\u65b9\u7a0b\uff08a-5\uff09x^2-4x-1=0\u6709\u5b9e\u6839\uff0c\u5219
\u5224\u522b\u5f0f\u25b3=\uff08-4\uff09^2-4(a-5)x(-1)\u300b0
\u5373\u25b3=16+4a-20\u300b0
4a\u300b20-16
4a\u300b4
a\u300b1
\u5219a\u7684\u53d6\u503c\u8303\u56f4\u4e3aa\u300b1\u4e14a\u22605
x^2+y^2-4x=0
即(x-2)^2+y^2=4
求y/(x+2)的取值范围，即求圆上的点(x,y)到点(-2,0)的斜率的取值范围，
从图上可以看出，分别上下相切时取最值，记上面的过(-2,0)的直线斜率为k1,下面的为k2,
分别连接圆心与两切点，
有k1=tan<OAB=OB/AB=2/√(4^2-2^2)=√3/3
k2=-√3/3
所以取值范围是[-√3/3,√3/3]
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