Question

Resolva a equação irracionais:
√3x+1+6=x

Answer 1

√3x + 1  + 6 = x
(√3x + 1)²  = (x - 6)²
3x + 1 = x² - 12x + 36
- x² + 12x - 36 + 3x + 1 = 0 (-1)
x² - 12x - 3x + 36 - 1 = 0
x² - 15x + 35 = 0
a = 1
b = - 15
c = 35
Δ = b² - 4.a.c
Δ = (-15)² - 4 . 1 . 35
Δ = 225 - 140
Δ = 85
x = - b + - √Δ/ 2a
x = - ( - 15 ) + - √85/ 2.1
x = 15 + - √85/2
x' = 15 + 9,219544 /2 ⇒x' = 12,11
x" = 15 - 9,219544/2  ⇒ x" = 2,89

verificando

√3x + 1 + 6 = x
√3 .12,11 + 1 + 6 = 12,11
√36,33 + 1 + 6 = 12,11
6,109828 + 6 = 12,11
12,11 = 12,11   verdadeira

√3x + 1 + 6 = x
√3( 2,89) + 1 + 6 = 2,89
√9,67 + 6 = 2,89
3,109662 + 6 = 2,89
9,11 = 2,89  falsa

S = { 12,11 }