Question

已知x=（根号2+1）/（根号2-1）,y=（根号3-1）/（根号3+1）,求x²-y²的值

Answer 1

x=（根号2+1）/（根号2-1）

=(√2+1)²／(2-1)

=2+1+2√2

=3+2√2

y=（根号3-1）/（根号3+1）

=﹙√3-1)²/(3-1)

=(3+1-2√3)/2

=2-√3

x²-y²

=(3+2√2)²-(2-√3﹚²

=9+8+12√2-(4+3-4√3)

=10+12√2+4√3