Question

encontre a maior raiz da equação x² -(2,333...)x + (1,333)=0
a)1
b)4/3
c)5/3
d)1/2

Answer 1

x² - (2,333...)x + (1,333) = 0

x = 2,333..
10x = 23,333
10x = 21 + 2,3333
10x = 21 + x
10x - x = 21
9x = 21
x = 21/9 ÷ 3
x = 7/3

logo, 2,333 = 7/3

x = 1,333
10x = 13,333
10x = 12 + 1,333
10x = 12 + x
10x - x = 12
9x = 12
x = 12/9 ÷ 3
x = 4/3

logo, 1,333.. = 4/3

a funçao será:

x² - 7x/3 + 4/3 = 0

∆ = b² - 4.ac
∆ = (- 7/3)² - 4.1.(4/3)
∆ = 49/9 - 16/3 mmc = 9
∆ = (49 - 48)/9
∆ = 1/9

x = -b±√∆ /2a
x = -(-7/3)±√1/9) /2.1
x = (7/3 ± 1/3) /2

x' = (7/3 + 1/3) /2
x' = 8/3/2
x' = 8/6 ÷ 2
x' = 4/3

x" = (7/3 - 1/3)/2
x" = (6/3)/2
x" = 2/2
x" = 1

sendo que 4/3 = 1,333 e é maior que 1

logo a maior raiz é 4/3

R.: Letra B