题目

若xy=3 ,x²+y²=16 那么x,y分别等于几?

提问时间：2020-08-02

答案

设点A = (x_0,y_0)
则 y_0 = 3/x_0
即 x_0 * y_0 = 3
OA = 4
即 (x_0)^2 + (y_0)^2 = 16
则 S_(△AOC) = 1/2 * x_0 * y_0 = 3/2
由于AB = BO
所以 L_(△ABC) = AC + AB + BC = AC + BO + BC = AC + OC = x_0 + y_0 = ((x_0)^2 + (y_0)^2 + 2 * x_0 * y_0)^(1/2) = (16 + 2 * 3)^(1/2) = √22