已知x,y为正整数,且满足2x^2+3y^2=4x^2y^2+1;则x^2+y^2=___

问题描述:

已知x,y为正整数,且满足2x^2+3y^2=4x^2y^2+1;则x^2+y^2=___
为什么“(y^2-1)/(2-4y^2)>=0”?

2x^2+3y^2=4x^2y^2+12x^2+3y^2-4x^2y^2-1=0 (1)y^2=(1-2x^2)/(3-4x^2)>=0 因为x为正整数得到x^2>=0.75或x^2=1再由(1)式可得x^2=(1-3y^2)/(2-4y^2)>=1得到(y^2-1)/(2-4y^2)>=0所以0.5