Question

2次根式题

已知a=根号3+根号2 b=根号3-根号2
1.a^2-ab+b^2
2.a^2-b^2

Answer 1

解：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

Answer 2

ab=3-2=1
a+b=2√3
a-b=2√2
a^2-ab+b^2=(a+b)^2-3ab=12-3=9
a^2-b^2=(a+b)(a-b)=2√3*2√2=4√6