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在解析几何的一些极值问题或者不等式问题中,恰当地运用不等式(a+b)(1/a+1/b)≥4(ab>0,可以使解题更简洁. [例1] 求圆x~2+y~2=r~2(r>0)的切线方程,使此切线夹在两坐标轴正半轴间的线段长最短,并求出这个线段长.
In some extreme problems or inequality problems of analytic geometry, using the inequality (a+b)(1/a+1/b)≥4 (ab>0) can make the problem more concise. [Example 1] The tangent equation of the circle x~2+y~2=r~2(r>0) makes the length of the line segment of the tangent sandwiched between the positive half axes of the two coordinate axes be the shortest, and finds the length of this line segment.