Question

Resolva A Equação X + 1/x = 5/2

Answer 1

x + 1/x = 5/2
m.m.c = x
x²/x + 1/ x = 5/2
x² + 1       5
-------  = ------
   x           2

5 x = 2 (x² + 1 )
2 x² + 2 = 5 x
2 x² + 2 - 5 x = 0
2 x² - 5 x + 2 = 0
Δ = b² - 4.a.c
Δ = (-5)² - 4 .2 . 2
Δ = 25 - 16
Δ = 9  ⇒√9 = 3
x = - b + ou - 3/2 .2
x´= -(-5) + 3/4 
x´= 5 + 3 / 4  ⇒5 + 3 /4 = 8/4 = 2
x´´ = 5 - 3/4 ⇒ 5 - 3/4 = 2/4 = 1/2
S = {2 ; 1/2 }