Question

Решите иррациональные уравнения (на выбор, не меньше трёх примеров).

Answer 1

Объяснение:

1)

$\sqrt{5 - 4x} = 5 \\ \sqrt{5 - 4x} {}^{2} = {5}^{2} \\ 5 - 4x = 25 \\ - 4x = 25 - 5 \\ - 4x = 20 \\ x = - 5$

2)

$3 - 2x = \sqrt{7x + 32 } \\ \sqrt{7x + 32} {}^{2} = (3 - 2x {)}^{2} \\ 7x + 32 = 9 - 12x + 4 {x}^{2} \\ - 4 {x}^{2} + 19x + 23 = 0 \\ d = (19 {)}^{2} - 4 \times ( - 4) \times 23 = 361 + 368 = 729 \\ x1 = \frac{ - 19 - 27}{ - 8} = \frac{ - 46}{ - 8} = \frac{23}{4} \\ x2 = \frac{ - 19 + 27}{ - 8} = \frac{8}{ - 8} = - 1$

окончательное решение -1

3)

$\sqrt{ {x}^{2} + 5x + 7} = \sqrt{5 {x}^{2} + 9x - 17} \\ \sqrt{ {x}^{2} + 5x + 7} {}^{2} = \sqrt{5 {x}^{2} + 9x - 17 } {}^{2} \\ {x}^{2} + 5x + 7 = 5 {x}^{2} + 9x - 17 \\ - 4 {x}^{2} - 4x + 24 = 0 \\ d = (4 {)}^{2} - 4 \times ( - 4) \times 24 = 16 + 384 = 400 \\ \\ x1 = \frac{4 + 20}{ - 8} = \frac{24}{ - 8} = - 3 \\ \\ x2 = \frac{4 - 20}{ - 8} = \frac{ - 16}{ - 8} = 2$

ответ: х1 = -3 , х2 = 2