Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 748

а) 4x⁴ – 17x² + 4 = 0
пусть х² = t
4t² – 17t + 4 = 0
D = (–17)² – 4 · 4 · 4 = 289 – 64 = 225
t = $$\frac{17 ± \sqrt{225}}{2 · 4}$$ = $$\frac{17 ± \sqrt{15}}{8}$$
t1 = 4; t2 = 2/8 = 1/4
x² = 4        или          x² = 1/4
x₁ = 2; x₂ = –2           x₃ = 1/2; x₄ = –1/2

б) 9x⁴ + 77x² – 36 = 0
пусть х² = t
9t² + 77t – 36 = 0
D = 77² – 4 · 9 · (-36) = 5929 + 1296 = 7225
t = $$\frac{-77 ± \sqrt{7225}}{2 · 9}$$ = $$\frac{-77 ± \sqrt{85}}{18}$$
t₁ = 8/18 = 4/9; t₂ = –2/8 = –1/4
x² = 4/9        или            x² = –1/4
x₁ = 2/3; x₂ = –2/3         корней нет

в) 2x⁴ – 9x² – 5 = 0
пусть х² = t
2t² – 9t – 5 = 0
D = (–9)² – 4 · 2 · (–5) = 81 + 40 = 121
t = $$\frac{9 ± \sqrt{121}}{2 · 2}$$ = $$\frac{9 ± \sqrt{11}}{4}$$
t₁ = 5; t₂ = –2/4 = –1/2
x² = 5            или           x² = –1/2
x₁ = $$\sqrt{5}$$; x₂ = –$$\sqrt{5}$$         корней нет

г) 6x⁴ = 5x² – 1 = 0
пусть х² = t
6t² – 5t – 1 = 0
D = (–5)² – 4 · 6 · (–1) = 25 + 24 = 49
t = $$\frac{5 ± \sqrt{49}}{2 · 6}$$ = $$\frac{5 ± \sqrt{7}}{12}$$
t₁ = 1; t₂ = –2/12 = –1/6
x² = 1            или            x² = –1/6
x₁ = 1; x₂ = –1                корней нет