Question

RESOLVA AS EQUAÇÕES DO SEGUNDO GRAU: A) x^2 – 5.x + 6 = 0 B) -2x^2 + 50 = 0 C) 10x^2 + 10.x = 0 D) x^2 – 10.x + 21 = 0

Answer 1

Oie, Td Bom?!

■ Resolvendo por fatoração.

A)

$x {}^{2} - 5x + 6 = 0$

$x {}^{2} - 2x - 3x + 6 = 0$

$x \: . \: (x - 2) - 3(x - 2) = 0$

$(x - 2) \: . \: (x - 3) = 0$

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$x - 2 = 0⇒x = 2$

$x - 3 = 0⇒x = 3$

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$S= \left \{ x_{1} = 2 \: , \: x_{2} = 3\right \}$

B)

$- 2x {}^{2} + 50 = 0$

$x {}^{2} - 25 = 0$

$(x - 5) \: . \: (x + 5) = 0$

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$x - 5 = 0⇒x = 5$

$x + 5 = 0⇒x = - 5$

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$S= \left \{ x_{1} = - 5 \: , \: x_{2} = 5 \right \}$

C)

$10x {}^{2} + 10x = 0$

$10x \: . \: (x + 1) = 0$

$x \: . \: (x + 1) = 0$

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$x = 0$

$x + 1 = 0⇒x = - 1$

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$S = \left \{x_{1} = - 1 \: , \: x_{2} = 0 \right \}$

D)

$x {}^{2} - 10x + 21 = 0$

$x {}^{2} - 3x - 7x + 21 = 0$

$x \: . \: (x - 3) - 7(x - 3) = 0$

$(x - 3) \: . \: (x - 7) = 0$

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$x - 3 = 0⇒x = 3$

$x - 7 = 0⇒x = 7$

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$S= \left \{x_{1} = 3 \: , \: x_{2} = 7 \right \}$

Att. Makaveli1996