Задание ЕГЭ
Решите уравнение x6 = –(7х + 10)3.Решение
Решение:
x6 = – (7x + 10)3
x6 = x2·3 = (x2)3 | –a3 = (–a)3
(x2)3 = (– (7x + 10))3
a3 = b3
a = b
x2 = – (7x + 10)
x2 = – 7x – 10
x2 + 7x + 10 = 0
D = 72 – 4·1·10 = 49 – 40 = 9 = 32
x_{1}=\frac{-7+3}{2\cdot 1 }=\frac{–4}{2}=-2\\x_{2}=\frac{-7-3}{2\cdot 1 }=\frac{-10}{2}=-5
Ответ: –2; –5.