Question

已知x,y为正整数,且2x^2+3x^2=4x^2y^2+1,则x^2+y^2=?

Answer 1

2x^2+3x^2?错了吧

2x^2+3y^2=4x^2y^2+1

2x^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