Question

Utilizando o método da fatoração determine a raíz da equação

d) x²-x-1/4=25​

Answer 1

Explicação passo-a-passo:

$\sf x^2-x-\dfrac{1}{4}=25$

$\sf x^2-2\cdot x\cdot\dfrac{1}{2}+\Big(\dfrac{1}{2}\Big)^2=25$

$\sf \Big(x-\dfrac{1}{2}\Big)^2=25$

$\sf x-\dfrac{1}{2}=\pm\sqrt{25}$

$\sf x-\dfrac{1}{2}=\pm5$

Há duas possibilidades:

1)

$\sf x-\dfrac{1}{2}=5$

$\sf x=5+\dfrac{1}{2}$

$\sf x=\dfrac{10+1}{2}$

$\sf \red{x'=\dfrac{11}{2}}$

2)

$\sf x-\dfrac{1}{2}=-5$

$\sf x=-5+\dfrac{1}{2}$

$\sf x=\dfrac{-10+1}{2}$

$\sf \red{x"=\dfrac{-9}{2}}$

O conjunto solução é:

$\sf S=\Big\{\dfrac{-9}{2},\dfrac{11}{2}\Big\}$