Question

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Решите уравнение
2x+3+√2x+3=2

Answer 1

Пошаговое объяснение:

$2x + 3 + sqrt{2x + 3} = 2$

$sqrt{2x + 3} = 2 - 2x - 3$

$sqrt{2x + 3} = - 1 - 2x$

$sqrt{2x + 3}^{2} = (- 1 - 2x)^{2}$

$2x + 3( - (1 + 2x)^{2}$

$2x + 3 = (1 + 2x) ^{2}$

$2x + 3 = 1 + 4x + 4x ^{2}$

$2x + 3 - 1 - 4x - 4x ^{2} = 0$

$- 2x + 2 - 4x^{2} = 0$

$- 4x ^{2} - 2x + 2 = 0$

$2x ^{2} + x - 1 = 0$

$2x ^{2} + 2x - x - 1 = 0$

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

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

$x + 1 = 0 \ 2x - 1 = 0$

$x = - 1 \ x = frac{1}{2}$

Проверяем:

$2( - 1) + 3 + sqrt{2 times ( - 1) + 3} = 2 \ 2 times frac{1}{2} + 3 + sqrt{2 times frac{1}{2} + 3 } = 2$

$2 = 2 \ 6 = 2$

$x = - 1$

x не равно 1/2

Ответ: x=-1