Question

已知a^2+a-1=0,求2a^3+4a^2+2的值；求（a-1/a)^2

Answer 1

a^2+a-1=0,所以a^2+a = 1

2a^3+4a^2+2

= 2a (a^2 + 2a) +2

= 2a (1 + a) + 2

= 2 (a + a^2) + 2

= 4

a^2+a-1=0,所以a^2 - 1 = a

(a-1/a)^2

= [(a^2 - 1)/a]^2

= [a/a]^2

= 1