Respuestas
Respuesta:
voy a utilizar múltiples métodos para resolver estas ecuaciones.
Explicación paso a paso:
1.- x² + 58x + 720 = 0
x. 18 = 18x
x. 40 = 40x
= 58x
(x + 18)(x + 40) = 0
X1 = -18 y X2 = -40
2.- x² + 3x + 2 = 0
X1 + X2 = -3 y X1 × X2 = 2
(-3/2 + u)(-3/2 - u) = 2
9/4 - 2 = u²
1/4 = u²
√(1/4) = 1/2 = u
X1 = -3/2 + 1/2 = -2/2 = -1
X2 = -3/2 - 1/2 = -4/2 = -2
3.- x² + 5x + 6 = 0
x. 3 = 3x
x. 2 = 2x
= 5x
(x + 3)(x + 2) = 0
X1 = -3 y X2 = -2
4.- 8x² + 7x + 2 = 0
X1 + X2 = -7/8 y X1 × X2 = 1/4
(-7/16 + u)(-7/16 - u) = 1/4
49/256 - 1/4 = u²
√( -15/256) = u
X1 = -7/16 + √(-15)/16 = [-7 + √(-15)]/16
X2 = -7/16 - √(-15)/16 = [-7 - √(-15)]/16
5.- 8x² - 10x + 3 = 0
∆ = (-10)² - 4(3)(8)
∆ = 100 - 96
∆ = 4
x = [b (+,-) √∆]/2a
x = [10 (+,-) √4]/16
X1 = [10 + 2]/16 = 12/16 = 3/4
X2 = [10 - 2]/16 = 8/16 = 1/2
4.- 4x² - 10x - 6 = 0
∆ = (-10)² - 4(-6)(4)
∆ = 100 + 96
∆ = 196
x = [b (+, -) √∆]/2a
x = [10 (+,-) √196]/8
X1 = (10 + 14)/8 = 24/8 = 3
X2 = (10 - 14)/8 = -4/8 = -1/2
5.- 3x² - 4x + 1 = 0
3x. -1 = -1x
x. -1 = -3x
= -4x
(3x - 1)(x - 1) = 0
X1 = 1/3 y X2 = 1