Question

o conjunto solução da equação (x-3/2)² = 1/4 é:

A) S= {-√10/2, √10/2}
B) S= {1, 2}
C) S= {-1, -2}
D) S= {7/4}
E) S= {3-√17/2, 3+√17/2}
conta por favor.​

Answer 1

Explicação passo-a-passo:

$\sf \left(x-\dfrac{3}{2}\right)^2=\dfrac{1}{4}$

$\sf x-\dfrac{3}{2}=\pm\sqrt{\dfrac{1}{4}}$

$\sf x-\dfrac{3}{2}=\pm\dfrac{1}{2}$

• $\sf x-\dfrac{3}{2}=\dfrac{1}{2}$

$\sf x=\dfrac{1}{2}+\dfrac{3}{2}$

$\sf x=\dfrac{1+3}{2}$

$\sf x=\dfrac{4}{2}$

$\sf x=2$

• $\sf x-\dfrac{3}{2}=-\dfrac{1}{2}$

$\sf x=-\dfrac{1}{2}+\dfrac{3}{2}$

$\sf x=\dfrac{-1+3}{2}$

$\sf x=\dfrac{2}{2}$

$\sf x=1$

$\sf S=\{1,2\}$

Letra B