Question

Resolva as equações do 20 grau abaixo no conjunto dos números reais: x²-3x-4=0

Answer 1

O valor de x nessa equação do segundo grau é:

$\boxed{ \red{4}}$

ou

$\boxed{ \green{ - 1}}$

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$\mathtt{\purple{Vamos~fazer!!!}}$

$\boxed{\begin{array}{lr} \mathtt{ \green{ {x}^{2} - 3x - 4 = 0 }}\end{array}}$

Sabendo que:

$\boxed{\begin{array}{lr} \green{ \mathtt{a}} = \red{1 }\\ \\ \mathtt{ \green{b}} = \red{ - 3} \\ \\ \mathtt{ \green{c} = \red{ - 4}}\end{array}}$

Valor de delta:

$\boxed{\begin{array}{lr}\Delta = \green{ \mathtt{ {b}^{2} - 4ac }} \\ \\ \Delta = 9 + 16 \\ \\ \Delta = \red{25}\end{array}}$

Valor de x:

$\boxed{\begin{array}{lr} \mathtt{x = \green{ \dfrac{ - b \pm \sqrt{\Delta} }{2} }} \\ \\ \\ \\ \mathtt{x = \dfrac{3 \pm5}{2} }\end{array}}$

Primeiro valor de x:

$\dfrac{8}{2} = \red{4}$

Segundo valor de x:

$\dfrac{ - 2}{2} = \green{ - 1}$

-

$\mathsf{\pink{Aprenda~mais~em:}}$

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$\boxed{\begin{array}{lr}\green{\infty}\mathbf{ \:By: Kponys}\end{array}}$

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$\Huge{\mathbb{\blue{Espero~ter~ajudado!!!}}}$

Answer 2

Olá,

$\Rightarrow\blue{\boxed{ \red{ \boxed{x_1 = 4}}}}$

$\Rightarrow\blue{\boxed{ \red{ \boxed{x_2 = -1}}}}$

Como resolver?

• Calcule o discriminante (∆); fórmula:

b² - 4ac

• Calcule o valor da incógnita (x); fórmula:

(-b ± √∆)/2a

• Encontre o resultado.

Resolução:

Sendo:

$a = 1$

$b = -3$

$c = -4$

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$\mathbf{\bold{\orange{\Delta = b^{2} - 4ac}}}$

$\mathbf{\bold{\purple{\Delta = -3^{2} - 4 \times 1 \times (-4)}}}$

$\mathbf{\bold{\gray{\Delta = 9 - 4 \times 1 \times (-4)}}}$

$\mathbf{\bold{\gray{\Delta = 9 - 4 \times (-4)}}}$

$\mathbf{\bold{\gray{\Delta = 9 - (-16)}}}$

$\mathbf{\bold{\blue{\Delta = 25}}}$

-

$\mathbf{\bold{\pink{x = \dfrac{-b \pm \sqrt{\Delta}}{2a}}}}$

$\mathbf{\bold{\green{x = \dfrac{-(-3) \pm \sqrt{25}}{2 \times 1}}}}$

$\mathbf{\bold{\red{x = \dfrac{3 \pm 5}{2}}}}$

-

$\mathbf{\bold{x_1 = \dfrac{3 + 5}{2}}}$

$\mathbf{\bold{x_1 = \dfrac{8}{2}}}$

$\mathbf{\bold{x_1 = 4}}$

-

$\mathbf{x_2 = \dfrac{\bold{3 - 5}}{2}}$

$\mathbf{x_2 = \dfrac{\bold{ - 2}}{2}}$

$\mathbf{x_2 = -1}$

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$\huge{\boxed{\bold{\green{Ass: Gold~Man}}}}$

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$\mathbf{\bold{\blue{Mais~informac_{\!\!\!,}\tilde{o}es~em:}}}$

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$\Huge{\mathbb{\red{ESPERO \: TER \: AJUDADO!}}}$