Question

O conjunto solução da equação (x-3/2)^2= 1/4 e:

Answer 1

• O conjunto solução da equação $\bf{\left({x-\dfrac{3}{2}}\right)^2=\dfrac{1}{4}}$  é  $\bf{(b)\;\;S=\{1,\;2\}}$.

 ➢  Nesse caso, vamos desenvolver a potência por meio de uma distributiva, ao obter uma equação do 2° grau, aplicaremos a fórmula de Bhaskara.

$\bf{\left({x-\dfrac{3}{2}}\right)^2=\dfrac{1}{4}}\\\\\\\bf{\left({x-\dfrac{3}{2}}\right)\cdot\left({x-\dfrac{3}{2}}\right)=\dfrac{1}{4}}\\\\\\\bf{x^2-\dfrac{3x}{2}-\dfrac{3x}{2}+\dfrac{9}{4}=\dfrac{1}{4}}\\\\\\\bf{\dfrac{4x^2-6x-6x+9=1}{4}}\\\\\\\bf{4x^2-12x+9-1=0}\\\\\\\bf{4x^2-12x+8=0}$

$\bf{Coeficientes:\;a=4,\;b=-12\;e\;c=8.}\\\\\\\bf{\Delta=b^2-4ac}\\\\\bf{\Delta=(-12)^2-4\cdot4\cdot8}\\\\\bf{\Delta=144-128}\\\\\bf{\Delta=16}\\\\\\\bf{x=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\\\\\bf{x=\dfrac{-(-12)\pm\sqrt{16}}{2\cdot4}}\\\\\\\bf{x=\dfrac{12\pm4}{8}}\\\\\\\bf{x_1=\dfrac{12+4}{8}=\dfrac{16}{8}=2}\\\\\\\bf{x_2=\dfrac{12-4}{8}=\dfrac{8}{8}=1}\\\\\\\\\boxed{\bf{S=\{1,\;2\}}}$

 ➢  Saiba mais em:

https://brainly.com.br/tarefa/28533066

Espero ter ajudado.

Bons estudos! :)