Question

若a=3+2倍根号2，b=3-2倍根号2，求a²b-ab²的值

Answer 1

ab=(3+2√2)*(3-2√2)=3^2 - (2√2)^2 =1 (平方差公式)
a-b=4√2
a²b-ab²=ab(a-b)=4√2

Answer 2

∵a=3+2倍根号2，b=3-2倍根号2，
∴a²b-ab²
=ab(a-b)
=(3+2倍根号2)(3-2倍根号2)(4倍根号2)
=4倍根号2