20a² - a - 30 = (4a - 5)(5a+6)
2b² +17b + 33 = (b + 3)(2b + 11)
x² - 4x - 45 = (x - 9)(x + 5)
3x³ - 21x² + 4x - 28 = 0
3x²·(x - 7) + 4·(x - 7) = 0
(x - 7)·(3x² + 4) = 0
x = 7
y³ + 11y² + 5y + 55 = 0
y²·(y + 11) + 5·(y + 11) = 0
(y + 11)(y² + 5) = 0
y = -11
Уравнения, являющиеся линейными:
x - 5y = 3y - 2
x/y - 5/(2y) = 3
1/x - 7y/(3x) = 2
(x⁴ - x²y² + 2x²y + y²)/(x² - xy + y) = (x⁴ + 2x²y + y² - x²y²)/(x² + y - xy) =
= ((x² + y)² - (xy)²)/(x² + y - xy) = (x² + y - xy)(x² + y + xy)/(x² + y - xy) =
= x² + y + xy
(x⁴ - 4x² + 2x²y² + y⁴)/(x² - 2x + y²) = (x⁴ + 2x²y² + y⁴ - 4x²)/(x² + y² - 2x) =
= ((x² + y²)² - (2x)²)/(x² + y² - 2x) = (x² + y² - 2x)(x² + y² + 2x)/(x² + y² - 2x) =
= x² + y² + 2x
(x² - 4x - 12)/(x + 2) = (x + 2)(x - 6)/(x + 2) = x - 6
(x² + 4x - 12)/(x + 6) = (x + 6)(x - 2)/(x + 6) = x - 2