有理数xy满足方程(1/2+√2/3)x+(1/3+√2/2)y=4+√2,则x-y=?

题目

有理数xy满足方程(1/2+√2/3)x+(1/3+√2/2)y=4+√2,则x-y=?

答案

∵(1/2+√2/3)x+(1/3+√2/2)y=4+√2
==>x/2+√2x/3+y/3+√2y/2=4+√2
∴(x/2+y/3)+(x/3+y/2)√2=4+√2
∵x和y是有理数
∴x/2+y/3=4,x/3+y/2=1
==>3x+2y=24,.(1),2x+3y=6.(2)
故由(1)式-(2)式,得x-y=18.