Question

若m＝根号2＋1,n＝1－根号2,求m²－mn＋n²的值

Answer 1

m＝√2＋1,n＝1－√2

m+n=2

m-n=2√2

mn=-1

m²－mn＋n²

=m(m+n)-2mn＋n²

=2m-2mn＋n²

==2m+2+n(m+n)-mn

=2m+2+2n+1

=2(m+n)+3

=7