Question

Find a^2+ 1/a^2,a^3+1/a^3 and a^4+1/a^4, if a+1/a=3​

Answer 1

Step-by-step explanation:

a+1/a=3

a^2+ 1/a^2

= (a)^2+(1/a)^2

= (a+1/a)^2 — 2*a*1/a

= (3)^2—2

= 9-2

= 7

a^3+1/a^3

= (a)^3+(1/a)^3

= (a+1/a)[(a)^2—a*1/a+(1/a)^2]

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

= 3[(a+1/a)^2 — 2*a*1/a]

=3[(3)^2—2]

= 3(9-2)

=21

a^4+1/a^4

= (a^2)^2+(1/a^2)^2

= (a^2+1/a^2)^2 — 2*a^2*1/a^2

=[ (a+1/a)^2—2*a*1/a ]^2— 2

= [(3)^2—2]^2—2

= (9-2)^2—2

= (7)^2—2

= 49—2

= 47