Question

if a²+1/a=4 show that a 6+1/a³=52​

Answer 1

a²+1/a=4

(a²+1/a)³= 4

(a²+1)³/a³=64

a^6+1+3×a²(a²+1)/a³ =64

a^6+1/a³+3a²(a²+1)/a³= 64

a^6+1/a³+3[a²+1/a]=64

a^6+1/a³+3×4=64

a^6+1/a³=64-12= 52