Question

若a-a分之1=2 ,怎么算代数式a3-a3分之1的值

Answer 1

a^3 -1/a^3=(a -1/a)(a^2 +1 +1/a^2).

由a -1/a= 2,

得：(a -1/a)^2= a^2 -2 +1/a^2=4,

即：a^2 +1 +1/a^2= 7.

所以：(a -1/a)(a^2 +1 +1/a^2)= 2 *7= 14

故：a^3 -1/a^3= 14.