Ce este (x / 4) - (2x / x + 2) = 1?

Răspuns:

# x = 5 + sqrt 33 # sau # x = 5-sqrt33 #

Explicaţie:

# x / 4- (2x) / (x + 2) = 1 #

#:. (x (x + 2) -4 (2x) = 4 (x + 2)) / (4 (x + 2)) #

# "multiplicați ambele părți prin" ## 4 (x + 2) #

#:. x (x + 2) -4 (2x) = 4 (x + 2) #

#:. x ^ 2 + 2x-8x = 4x + 8 #

#:. x ^ 2 + 2x-8x-4x-8 = 0 #

#:. x ^ 2-10x-8 = 0 #

# "formula patratică: -" #

#: x = (- b + -sqrt (b ^ 2-4ac)) / (2a) #

#:. a = 1, b = -10, c = -8 #

#:. x = (- (- 10) + - sqrt ((-10) ^ 2-4 (1) (- 8))) / 2 #

#:. x = (10 + - sqrt (132)) / 2 #

#: x = (10 + - sqrt (33 * 2 * 2)) / 2 #

#:. x = (10 + - 2 sqrt (33)) / 2 #

#:. x = 5 + - sqrt 33 #

#:. x = 5 + sqrt 33 sau x = 5 sqrt 33 #