July 2022 1 17 Report
x= 4+ √x+8
[tex]x = 4 + \sqrt{x + 8} [/tex]
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Mrdenk
MrdenkMrdenk

Так как я не понял, какой из примеров нужный, сделаем оба:

1)

x = 4 + \sqrt{x} + 8

x = 12 + \sqrt{x}

ОДЗ: x >= 0

Пусть

y = \sqrt{x}

Тогда

{y}^{2} = 12 + y

{y}^{2} - y - 12 = 0

D = 1 + 48 = 49

y1 = (1 + 7) / 2 = 4

y2 = (1 - 7) / 2 = -3 Не подходит, так как y >= 0

\sqrt{x} = 4

Откуда

X = 16

Ответ: x = 16

Второй:

x = 4 + \sqrt{x + 8}

ОДЗ: x >= -8

x - 4 = \sqrt{x + 8}

x - 4 >= 0

{x}^{2} - 8x + 16 = x + 8

{x}^{2} - 9x + 8 = 0

{x}^{2} - 8x - x + 8 = 0

x(x - 8) - 1(x - 8) = 0

(x - 1)(x - 8) = 0

X1 = 1 не подходит, так как x - 4 = -3, то есть меньше 0

X2 = 8

Ответ: x = 8

1 votes Thanks 0
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