Matéria: Matemática
Autor: carlosohveilerdutra
Perguntado 3 anos atrás

Resolva as equações do 2° grau a seguir:

a) x² - 5x + 6 = 0

b) x² - 8x + 12 = 0

c) x² + 2x - 8 = 0

d) 2x² - 8x + 8 = 0

e) x² - 4x - 5 = 0

Respostas

respondido por: Anônimo

$\large\boxed{\begin{array}{lr}c) \\ A = 1 B = 2 C = -8 \\ \\ Δ = B {}^{2} - 4.A.C \\ Δ = 2 {}^{2} - 4.1.(-8) \\ Δ = 4 + 32 \\ Δ = 36 \\ \\ X = -B +- √Δ / 2.A \\ X = -2 +- √36 / 2.1 \\ X = -2 +- 6 / 2 \\ \\ X| = -2 + 6 / 2 \\ X| = 4 / 2 \\ X| = 2 \\ \\ X|| = -2 - 6 / 2 \\ X|| = -8 / 2 \\ X|| = -4 \\ \end{array}}$

$\large\boxed{\begin{array}{lr}a) \\A = 1 B = -5 C = 6 \\ \\ Δ = B {}^{2} - 4.A.C \\ Δ = (-5) {}^{2} - 4.1.6 \\ Δ = 25 - 24 \\ Δ = 1 \\ \\ X = -B +- √Δ / 2.A \\ X = -(-5) +- √1 / 2.1 \\ X = 5 +- 1 / 2 \\ \\ X| = 5 + 1 / 2 \\ X| = 6 / 2 \\ X| = 3 \\ \\ X|| = 5 - 1 / 2 \\ X|| = 4 / 2 \\ X|| = 2 \\ \end{array}}$

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$\large\boxed{\begin{array}{lr}b) \\A = 1 B = -8 C = 12 \\ \\ Δ = B {}^{2} - 4.A.C \\ Δ = (-8) {}^{2} - 4.1.12 \\ Δ = 64 - 48 \\ Δ = 16 \\ \\ X = -B +- √Δ / 2.A \\ X = -(-8) +- √16 / 2.1 \\ X = 8 +- 4 / 2 \\ \\ X| = 8 + 4 / 2 \\ X| = 12 / 2 \\ X| = 6 \\ \\ \\ X|| = 8 - 4 / 2 \\ X|| = 4 / 2 \\ X|| = 2 \end{array}}$

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$\large\boxed{\begin{array}{lr}d) \\ A = 2 B = -8 C = 8 \\ \\ Δ = B {}^{2} - 4.A.C \\ Δ = (-8) {}^{2} - 4.2.8 \\ Δ = 64 - 64 \\ Δ = 0 \\ \\ X = -B +- √Δ / 2.A \\ \\ X| = X|| = -8 / 4 \\ X| = X|| = -2 \\ \end{array}}$

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$\large\boxed{\begin{array}{lr}A = 1 B = -4 C = -5 \\ \\ Δ = B {}^{2} - 4.A.C \\ Δ = (-4) {}^{2} - 4.1.(-5) \\ Δ = 16 + 20 \\ Δ = 36 \\ \\ X = -B +- √Δ / 2.A \\ X = -(-4) +- √36 / 2.1 \\ X = 4 +- 6 / 2 \\ \\ X| = 4 + 6 / 2 \\ X| = 10 / 2 \\ X| = 5 \\ \\ X|| = 4 - 6 / 2 \\ X|| = -2 / 2 \\ X|| = -1 \\ \end{array}}$