Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 751

а) 1/8x³ = 1
(1/2x)³ = 1³
1/2x = 1
x = 2

б) 1000x³ + 1 = 0
1000x³ = –1
(10x)³ = (–1)³
10x = –1
x = –0,1

в) 1/27x³ = 0,001
(1/3x)³ = 0,1³
1/3x = 1/10
x = 1/10 : 1/3 = 1/10 · 3 = 3/10 = 0,3

г) 1/9x⁴ – 16 = 0
(1/3x²)² = 4²
1/3x² = 4
x² = 4 : 1/3 = 4 · 3 = 12
x₁ = $$\sqrt{12}$$ = 2$$\sqrt{3}$$
x₂ = –$$\sqrt{12}$$ = –2$$\sqrt{3}$$

д) 1 + x⁵ = 0
x⁵ = –1
x⁵ = (–1)⁵
x = –1

е) x⁸ – 16 = 0
x⁸ = 16
(x²)⁴ = 24
x² = 2
x₁ = $$\sqrt{2}$$
x₂ = –$$\sqrt{2}$$