Question

设X,Y都是有理数,并且X,Y满足X2+Y+Y√2=17-4√2.求X+Y的值

Answer 1

X2+Y+Y√2=17-4√2

(x2+y-17)+(y+4)√2=0

(x2+y-17)=-(y+4)√2

可以知道,X,Y都是有理数,

所以(x2+y-17)是有理数,同样等式右边也得是有理数.

等式右边是-(y-4)√2,要是有理数,

只有-(y+4)√2=0

y=-4,

所以x2+y-17=0

x2=21

x=21/2