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已知直线l过点p(2,3),并且直线l与x轴,y轴的正半轴分别交于A、B两点,求三角形面积的最小值以及此时直线l的方程。解法一:分析:设出直线方程的截距式,并且写出面积的表达式,把点p的坐标代入直线方程得到a与b的等量关系,再利用基本不等式求出ab的范围,进而得出面积的最小值以及直线方程。在利用基本不等式求最值时,注意基本不等式应用的条件是“一正、二定、三相等”。
It is known that the straight line l passes through point p (2,3), and the positive semi-axes of the line l and the x-axis and the y-axis are respectively intersected with points A and B to find the minimum value of the area of the triangle and the equation of the line l at this moment. Solution 1: Analysis: set up the intercept of linear equations, and write the expression of area, the coordinates of point p into the linear equation to obtain the equal relationship between a and b, and then use the basic inequality to find the scope of ab, and thus Obtain the minimum of the area and the equation of the line. When using the basic inequality to find the most value, pay attention to the basic inequalities applied condition is “one positive, two fixed, three equal ”.