Question

(UFPR) resolva a equação (n+1)/(n-1)=6(n-1)

Answer 1

n+1/n-1 = 6n-6
n+1 = (6n-6).(n-1)
n+1 = 6n² - 6n - 6n + 6 
n+1 = 6n² - 12n +6
n+1-6n²+12n-6 = 0

-6n² + 13n - 5 = 0

Δ = 169 - 120
Δ = 49

x = -13 +-√49/-12
n = -13+-7/-12
n' = -13+7/-12
n' = -6/-12 = 1/2

n'' = -13-7/-12
n'' = -20/-12 = 5/3        
                                     S = { 5/3 , 1/2 }     ok

Answer 2

Aqui vc ira fazer o meio pelos os extremos que vai ficar
(n-1)*6(n-1)=n+1
(n-1)*6n-6=n+1
6n²-6n-6-n+6=n+1
6n²-12n+6=n+1
6n²-12n+6-n-1=0
6n²-13+5=0
aplica Baskara
x'=13+7/12=5/3
x''=13-7/12=1/2.