Question

02-0 conjunto verdade da equação 10x2 - 7x + 1 = 0 é:
a) V= {1/2, -1/5)
b) V= {-1/2, 1/5}
c) V= {1/2, 1/5)
d) V = {-1/2, -1/5)
e) V=Ø
I

Answer 1

Resposta: $\text{V}=\left\{\dfrac{1}{5},\dfrac{1}{2} \right\} \ \ \text{alternativa c}$

Explicação passo-a-passo:

$10x^2-7x+1=0$

Utilizando a fórmula de Bhaskara, onde

$a=10\\b=-7\\c=1$

Temos

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot10\cdot1}}{2\cdot10}$

$x=\dfrac{7\pm\sqrt{49-40}}{20}$

$x=\dfrac{7\pm\sqrt{9}}{20}$

$x=\dfrac{7\pm3}{20}$

$x'=\dfrac{7+3}{20}=\dfrac{10}{20}=\dfrac{10\div10}{20\div10}=\dfrac{1}{2}$

$x''=\dfrac{7-3}{20}=\dfrac{4}{20}=\dfrac{4\div4}{20\div4}=\dfrac{1}{5}$

$\text{V}=\left\{\dfrac{1}{5},\dfrac{1}{2} \right\} \ \ \text{alternativa c}$