Question

Resolva as seguintes equações do 2º grau:
a) 9x²-16-01
b) x²-x-0 ​

Answer 1

Resposta:

$a:\ x=\frac{8+\sqrt{73}}{9}\ ou\ x=\frac{8-\sqrt{73}}{9}\\\\b:\ x=1\ ou\ x=0$

Explicação passo a passo:

$a)\\\\9x^2-16x-1=0\\\\a=9,\ b=-16\ e\ c=-1\\\\x_{1,2}=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\\\x_{1,2}=\frac{-(-16)\±\sqrt{(-16)^2-4(9)(-1)}}{2(9)}\\\\x_{1,2}=\frac{16\±\sqrt{256+36}}{18}\\\\x_{1,2}=\frac{16\±\sqrt{292}}{18}\\\\x_{1,2}=\frac{16\±\sqrt{2\bullet2\bullet73}}{18}\\\\x_{1,2}=\frac{16\±\sqrt{2^2\bullet73}}{18}\\\\x_{1,2}=\frac{16\±2\sqrt{73}}{18}\\\\x_{1,2}=\frac{8\±\sqrt{73}}{9}\\\\x_{1}=\frac{8+\sqrt{73}}{9}\ e\ x_{2}=\frac{8-\sqrt{73}}{9}$

$b)\\\\x^2-x=0\\\\a=1,\ b=-1\ e\ c=0\\\\x_{1,2}=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\\\x_{1,2}=\frac{-(-1)\±\sqrt{(-1)^2-4(1)(0)}}{2(1)}\\\\x_{1,2}=\frac{1\±\sqrt{1-0}}{2}\\\\x_{1,2}=\frac{1\±\sqrt{1}}{2}\\\\x_{1,2}=\frac{1\±1}{2}\\\\x_{1,2}=\frac{1+1}{2}=\frac{2}{2}=1\ e\ x_{2}=\frac{1-1}{2}=\frac{0}{2}=0$

Answer 2

Resposta:

Deve corrigir o enunciado para:

a) 9x²-16= 0

b) x²-x = 0

Explicação passo a passo:

Resolva as seguintes equações do 2º grau:

a) 9x²-16= 0

9x^2 = 16

x^2 = 16/9

X = \/(16/9)

x = +/- 4/3

R.: s = {4/3; -4/3}

_______________

b) x²-x = 0

x.(x-1)= 0

x = 0

x - 1 = 0

x = 1

R.:

X = 0

X = 1