Question

实数X、Y满足2X平方+Y平方+1=3X,则X平方+Y平方 的最大值是

Answer 1

设t=x^2+y^2

y^2=t-x^2

2X平方+Y平方+1=3X,

2x^2+t-x^2-3x+1=0

x^2-3x+t+1=0

判别式=9-4(t+1)=5-4t>=0

t