Question

设实数x、y满足方程2x^2+3y^2=6y,求x+y的最大值 急求！！

Answer 1

2x^2+3y^2=6y
2x^2+3(y-1)^2-=3
x^2/仔姿卜3+(y-1)^2/2=0.5
x=√1.5cost , y=sint+1
x+y=√1.5cost +sint+1
=√10/2sin(t +p) p=arctan(√册数1.5 )
x+y的最大念穗值=√10/2+1

Answer 2

配方得：2x^2/3+(y-1)^2=1
参数法：x=acost, y=1+sint, a=√(3/2)
因此裤梁旦有：x+y=acost+1+sint=1+√(a^2+1)sin(t+p)=1+√胡扰(5/2)sin(t+p), 其中p=arctana
故最大值为1+√(5/渣伏2)

Answer 3

等于1