Question

Resolva a equação incompleta do segundo grau

$2 \times {}^{2} - 3 = 0$
​

Answer 1

Explicação passo-a-passo:

$\sf 2x^2-3=0$

$\sf 2x^2=3$

$\sf x^2=\dfrac{3}{2}$

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

• $\sf x'=\sqrt{\dfrac{3}{2}}$

$\sf x'=\dfrac{\sqrt{3}}{\sqrt{2}}$

$\sf x'=\dfrac{\sqrt{3}}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}$

$\sf \red{x'=\dfrac{\sqrt{6}}{2}}$

• $\sf x"=-\sqrt{\dfrac{3}{2}}$

$\sf x"=\dfrac{-\sqrt{3}}{\sqrt{2}}$

$\sf x"=\dfrac{-\sqrt{3}}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}$

$\sf \red{x"=\dfrac{-\sqrt{6}}{2}}$

O conjunto solução é:

$\sf S=\Big\{\dfrac{-\sqrt{6}}{2},\dfrac{\sqrt{6}}{2}\Big\}$