Question

A terça parte de um número adicionado ao quádruplo do quadrado desse número é igual a dois.

Answer 1

$\frac{x}{3}+4\cdot x^2=2\\\\x+12x^2=6\\\\12x^2+x-6=0\\\\\\\Delta=b^2-4ac\\\\\Delta=1^2-4\cdot12\cdot(-6)\\\\\Delta=289\\\\\\x=\frac{-b\pm\sqrt\Delta}{2a}\\\\x=\frac{-1\pm17}{24}\\\\\boxed{x_1=\frac{2}{3}}\\\\\boxed{x_2=-\frac{3}{4}}$

Answer 2

x/3 + 4 x² = 2
m.m.c = 3
x/3 + 12 x²/3 = 6/3
eliminar o denominador devido a igualdade
x + 12 x² = 6
12 x² + x - 6 = 0
Δ = b² - 4.a.c
Δ = 1² - 4 . 12. -6
Δ = 1 + 288
Δ = 289 ⇒√289 = 17
x = - b + ou - 17/2.12
x´= -1 + 17/24⇒16/24 = 2/3
x´´ = -1 - 17 /24 ⇒ -18/24 = - 3/4
S = {-3/4 ; 2/3 }