Question

Stiind ca a+1 supra a =4 ,a = taiat 0, calculeaza ala a -II a+1 supra a la a-II a . Rezultatul este?
Ajutati-ma! Va rog!

Answer 1

a+1/a=4
(a²+1)/a=4
a²+1=4a
a²-4a+1=0
Δ=16-4=12
a₁=(4-2√3)/2=2(2-√3)/2=2-√3
a₂=(4+2√3)/2=2(2+√3)/2=2+√3
daca a=2-√3
a²+1/a²=(2-√3)²+1/(2-√3)²=4-4√3+3+1/(4-4√3+3)=7-4√3+1/(7-4√3)=
=7-4√3+(7+4√3)/(49-48)=7-4√3+7+4√3=14
a²+1/a²=14

daca a=2+√3
a²+1/a²=(2+√3)²+1/(2+√3)²=7+4√3+1/(7+4√3)=7+4√3+(7-4√3)/(49-48)=
7+4√37-4√3=14

concluzie
a²+1/a²=14