Question

given that,
a+1/a = 2

prove that , a^3 + 1/a^3 = a^4 + 1/a^4


step by step,
anyone could answer as bangladesh's math rule it will be very helpful.

because I'm from bangladesh.

Answer 1

a+1/a=2
a^2-2a+1=0
(a-1)^2=0
therefore a=1
a^3+1/a^3=2
and a^4+1/a^4=×

Answer 2

a+1/a=2
a^2+1=2a
a^2-2a+1=0
a^2-a-a+1=0
a(a-1)-1(a-1)
a=1
to prove
a^3+1/a3=a^4+1/a^4
taking LHS
a^3+1/a3
=1^3+1/1^3
=1+1/1
=(1+1)/1
=2
taking RHS
a^4+1/a^4
=1^4+1/1^4
=1+1/1
=(1+1)/1
=2
2=2
H.P