Question

como resolver x²-5x/4=3/2​

Answer 1

Olá, boa tarde!

Resposta:

$\boxed{\color{red}{\mathsf{x' \ \longrightarrow \ x=\dfrac{5+11}{8} \ \longrightarrow \ x=\dfrac{16^{~ :2}}{8^{~ :2}} \ \longrightarrow \ x=2}}}$

$\boxed{\color{red}{\mathsf{x" \ \longrightarrow \ x=\dfrac{5-11}{8} \ \longrightarrow \ x=-\dfrac{6^{~ :2}}{8^{~ :2}} \ \longrightarrow \ x=-\dfrac{3}{4}}}}$

Explicação passo-a-passo:

$\mathsf{x^2 - \dfrac{5x}{4} = \dfrac{3}{2}}$

$\mathsf{x^2 - \dfrac{5x}{4} - \dfrac{3}{2} =0}$

Propriedade Distributiva

$\mathsf{4x^2 +4 (-\dfrac{5x}{4} )+4(-\dfrac{3}{2}) =0}$

$\mathsf{4x^2 +\cancel{4}(-\dfrac{5x}{\cancel{4}} )+\cancel{4}(-\dfrac{3}{\cancel{2}}) =0}$

$\mathsf{4x^2 -5x -6=0}$

Bhaskara

a = 4

b = - 5

c = - 6

$\mathsf{x= \dfrac{5 \pm \sqrt{(-5)^2 -4 \cdot (4 \cdot -6)}}{8}}$

$\mathsf{x =\dfrac{5 \pm \sqrt{25 -4 \cdot -24}}{8}}$

$\mathsf{x =\dfrac{5 \pm \sqrt{25+96}}{8}}$

$\mathsf{x =\dfrac{5 \pm \sqrt{121}}{8}}$

$\mathsf{x =\dfrac{5 \pm 11}{8}}$

$\mathsf{x' \ \longrightarrow \ x=\dfrac{5+11}{8} \ \longrightarrow \ x=\dfrac{16^{~ :2}}{8^{~ :2}} \ \longrightarrow \ x=2}$

$\mathsf{x" \ \longrightarrow \ x=\dfrac{5-11}{8} \ \longrightarrow \ x=-\dfrac{6^{~ :2}}{8^{~ :2}} \ \longrightarrow \ x=-\dfrac{3}{4}}$

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

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