Question

2次根式题已知a=根号3+根号2 b=根号3-根号21.a^2-ab+b^22.a^2-b^2

Answer 1

a²-ab+b²

=(√3+√2)²-(√3+√2)(√3-√2)+(√3-√2)²

=(√3)²+2√3×√2+(√2)²-[(√3)²-(√2)²]+(√3)²-2√3×√2+(√2)²

=3+2√6+2-(3-2)+3-2√6+2

=3+2-1+3+2

=9

a²-b²

=(√3+√2)²-(√3-√2)²

=[(√3+√2)+(√3-√2)][(√3+√2)-(√3-√2)]

=(√3+√2+√3-√2)(√3+√2-√3+√2)

=2√3×2√2

=4√6