Question

已知:a^2-b^2=(a-b)(a+b);a^3-b^3=(a-b)(a^2+ab+b^2);a^4-b^4=(a-b)(a^3+a^2b+ab^2+b^3)...

(1)根据你发现的规律填空:a^5-b^5=(a-b)(___________).
(2)若a-1/a=2,请根据上述规律求代数式a^3-1/a^3的值.

Answer 1

a^5-b^5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4).

a^3-1/a^3=(a-1/a)(a^2+1+1/a^2)
=2[(a-1/a)^2+3]
=14

Answer 2

a^5-b^5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4).

a^3-1/a^3=(a-1/a)(a^2+1+1/a^2)
=2[(a-1/a)^2+3]
=14
将立方改为平方，
再计算

Answer 3

a~5-b~5=(a-b)(a~4+a~3b+a~2b~2+ab~3+b~4),a~3-1/a~3=(a-1/a)(a~2+1+1/a~2)=2((a-1/a)~2+3)=14

Answer 4

a^5-b^5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4).
14

Answer 5

14