Question

Alguém sabe resolver até o final?
x2 – 5mx + 6m2 = 0​

Answer 1

Olá, boa noite!

Resposta:

$\boxed{\color{red}{\mathsf{x'=3m}}}$

$\boxed{\color{red}{\mathsf{x"=2m}}}$

Explicação passo-a-passo:

$\mathsf{x^2 -5mx+6m^2 =0}$

a = 1

b = - 5m

c = $\mathsf{6m^2}$

$\mathsf{x =\dfrac{5m \pm \sqrt{(-5m)^2 -4 \cdot (1 \cdot (6m^2))}}{2}}$

$\mathsf{x= \dfrac{5m \pm \sqrt{25m^2 -4 \cdot (6m^2)}}{2}}$

$\mathsf{x= \dfrac{5m \pm \sqrt{25m^2 -24m^2}}{2}}$

$\mathsf{x= \dfrac{5m \pm \sqrt{m^2}}{2}}$

$\mathsf{x= \dfrac{5m \pm \sqrt[2]{m^2 }}{2}}$

$\mathsf{x= \dfrac{5m \pm \sqrt[\cancel{2}]{m^{\cancel{2}}}}{2}}$

$\mathsf{x= \dfrac{5m \pm m}{2}}$

$\mathsf{x'= \dfrac{5m + m}{2} \ \longrightarrow \ x' = \dfrac{6m}{2} \ \lonrightarrow \ x'=3m}$

$\mathsf{x"= \dfrac{5m-m}{2} \ \lonrightarrow \ x"= \dfrac{4m}{2} \ \longrightarrow \ x"=2m}$

==================== Espero ter ajudado ====================

Abraços!