由3x^2＋2y^2=6x得：y^2 = (6x-3x^2)/2
x^2+y^2 = x^2 + (6x-3x^2)/2 = -1/2x^2 + 3x = -1/2(x-3)^2 + 4.5 ≤ 4.5
最大值4.5配方大家都会……极坐标与参数方程呢？【上面少做了一步求x定义域，6x-3x^2=2y^2≥0，x定义域：0≤x≤24.5有误，最大值应为4】3x^2＋2y^2=6x移项：3x^2-6x＋2y^2=0配方：3(x-1)^2 -3 +2y^2 = 03(x-1)^2 +2y^2 = 3两边同除以3：(x-1)^2 +{ y/{根号(3/2)} }^2 = 1令x-1=cost，y/{根号(3/2)} =sint得到参数方程如下：x = 1+costy=根号(3/2)sintx^2+y^2=(1+cost)^2 + 3/2 sin^2t=1+2cost+cos^2t + 3/2(1-cos^2t)= -1/2cos^2t + 2cost + 5/2=-1/2(cost-2)^2 + 9/2-1 ≤ cost ≤ 1-3 ≤ cost-2 ≤ -11/2 ≤ 1/2(cost-2)^2 ≤ 9/20 ≤ -1/2(cost-2)^2 +9/2 ≤ 4故x^2+y^2最大值4最大值为4的话……答案错误……用两种方法做出来结果都是4，如果答案4.5的话，就是答案错了