Question

Resolver las siguientes ecuaciones:

a)(x-5)(x+1)+5=0

b)3(x-1)(x+2)=3x-6

c)21x-100=x^{2} +21-x

d)2x^{2} -1=1-x-x^{2}

Answer 1

Respuesta:

a) x = 0 ∧ x = 4

b) x = 0

c) x = 11

d) x = -1 ∧ x = 2/3

Explicación paso a paso:

a)

(x-5)(x+1)+5=0

x² + x -5x - 5 + 5  = 0

x² - 4x = 0

x(x-4) = 0

x = 0 ∧ x = 4

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b)

3(x-1)(x+2)=3x-6

x² + 2x - x - 2 = (3x-6 )/3

x² + x - 2 = x - 2

x² = 0

x = 0

c)

21x-100=x^{2} +21-x

0 = x² - 21x - x + 21 + 100

0 = x² - 22x + 121

0 = ( x -11) (x-11)

x = 11

d)

2x^{2} -1=1-x-x^{2}

2x² +x² + x - 1 - 1 = 0

3x² + x - 2 = 0

(3x-2)(x+1) = 0

x = 2/3 ∧ x = -1