Question

Решите 2 уравнение:
8) (x-2)²-25=0
10) (3x+4)²-50=0; Тэарэму Виета не изучали

Answer 1

(x-2)²-25=0
(x-2)² = 25
х-2 = ±√25
х-2 = ±5
х = ±5 + 2
х₁ = -5 + 2 = -3
х₂ = 5 + 2 = 7

(3x+4)²-50=0
(3x+4)² = 50
3x+4 = ±√50
3x+4 = ±5√2
3х = ±5√2 - 4
х₁ = -(5√2 - 4)/3
х₂ = (5√2 - 4)/3

Answer 2

(x - 2)² - 25 = 0
(x - 2)² - 5² = 0
(x - 2 - 5)(x - 2 + 5) = 0
(x - 7)(x + 3) = 0
или   x - 7 = 0   ⇒  x = 7
или   x + 3 = 0  ⇒  x = - 3
Ответ: - 3 , 7

(3x + 4)² - 50 = 0
9x² + 24x + 16 - 50 = 0
9x² + 24x - 34 = 0
D = 24² - 4 * 9 * (- 34) = 576 + 1224 = 1800
$x _{1} = \frac{-24+ \sqrt{1800} }{18}= \frac{-24+ \sqrt{900*2} }{18}= \frac{-24+30 \sqrt{2} }{18}= \frac{-4+5 \sqrt{2} }{3}\\\\x _{2} = \frac{-24- \sqrt{1800} }{18}= \frac{-24-30 \sqrt{2} }{18}= \frac{-4-5 \sqrt{2} }{3}$