Question

ejercicios de matematicas:
Resuelva las siguientes ecuaciones:

1+x=3-x

6y-5(1+2y)=3+2(1-y)

reduzca las siguientes ecuaciones y reduzcalas:

(x-4)^2=(x-2)^2

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

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

Answer 1

a)
1 + X = 3 - X

2X = 3 - 1

2X = 2

X = 1

b)

6Y - 5(1+ 2Y) = 3 + 2(1 - Y)

6Y - 5 - 10 Y = 3 + 2 - 2Y

-4Y - 5 = 3 + 2 - 2Y

-4Y + 2Y = 3 + 2 + 5

-2Y = 10

Y = 10/-2

Y = -5

c)
(X - 4)² = (X - 2)²

X² - 8X + 16 = X² - 4X + 4

X² - X² + 16 - 4 = 8X - 4X

12 = 4X

X = 12/4

X = 3

d)
(X - 1)(X + 3) = (X + 2)(X - 3) +1

(X - 1)(X + 3) = X² + 3X - X - 3 = X² + 2X - 3

(X + 2)(X - 3) + 1 = X² - 3X + 2X - 6 + 1 = X² - X - 5

X² + 2X - 3 =  X² - X - 5

X² - X² + 2X + X = - 5 + 3

3X = - 2

X = -2/3

e)

(X + 1)³ + (X - 1)³ = 2X³

(X + 1)³  = X³ + 3X² + 3X + 1

(X - 1)³ = X³ - 3X² + 3X - 1
 
X³ + 3X² + 3X + 1 + X³ - 3X² + 3X - 1 = 2X³ + 6X

2X³ + 6X = 2X³

2X³ - 2X³ + 6X = 0

6X = 0

X = 0