Решите уравнения: 1) x (x^2-2x)= x^3-8 2) (х+7)(х-7)+(х-3)^2=53 3) 3\x+2=8\3-x

Question

Решите уравнения:
1) x (x^2-2x)= x^3-8
2) (х+7)(х-7)+(х-3)^2=53
3) 3\x+2=8\3-x

Answer 1

Х(х² - 2х) = х³ - 8
х³ - 2х² - х³ + 8 = 0
х² = 4
х = ±2

(х + 7)(х - 7) + (х - 3)² = 53
х² - 49 + х² - 6х + 9 - 53 = 0
2х² - 6х - 93 = 0
х = (6 ± √(36 + 4×2×93))/4 = (3 ± √195)/2

3/х + 2 = 8/(3 - х) | × х(3 - х) ≠ 0
3(3 - х) + 2х(3 - х) = 8х
9 - 3х + 6х - 2х² - 8х = 0
2х² + 5х - 9 = 0
х = (-5 ± √(25 + 4×2×9))/4 = (-5 ± √97)/4