Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 635

а) 1) 2x − 1/x + 6 = 5 ОДЗ: x + 6 ≠ 0, x ≠ −6 2x − 1/x + 6 = 5/1 2x − 1 = 5(x + 6) 2x − 5x = 30 + 1 −3x = 31 x = 31 : (−3) x = −101/3
2) 2x − 1/x + 6 = −3 ОДЗ: x + 6 ≠ 0, x ≠ −6 2x − 1/x + 6 = −3/1 2x − 1 = −3(x + 6) 2x + 3x = −18 + 1 5x = −17 x = −17 : 5 x = −3,4
3) 2x − 1/x + 6 = 0 ОДЗ: x + 6 ≠ 0, x ≠ −6 2x − 1/x + 6 = 0 2x − 1 = 0 2x = 1 x = 1 : 2 x = 0,5
4) 2x − 1/x + 6 = 2 ОДЗ: x + 6 ≠ 0, x ≠ −6 2x − 1/x + 6 = 2/1 2x − 1 = 2(x + 6) 2x − 2x = 12 + 1 0x = 13 Нет решений
б) 1) x² + х − 2/x + 3 = −10 ОДЗ: x + 3 ≠ 0, x ≠ −3 x² + х − 2/x + 3 = −10/1 x² + х − 2 = −10(x + 3) x² + х − 2 + 10x + 30 = 0 x² + 11x + 28 = 0 D = b² − 4ac = 11² − 4 ⋅ 1 ⋅ 28 = 121 − 112 = 9 > 0 имеет 2 корня
x₁ = $$ \frac{-b+\sqrt{D}}{2 a}=\frac{-11+\sqrt{9}}{2 ⋅ 1} $$ = −11 + 3/2 = −8/2 = −4 x₂ = $$ \frac{-b-\sqrt{D}}{2 a}=\frac{-11-\sqrt{9}}{2⋅ 1} $$ = −11 − 3/2 = −14/2 = −7
x₁ = −4, x₂ = −7
2) x² + х − 2/x + 3 = 0 ОДЗ: x + 3 ≠ 0, x ≠ −3 x² + х − 2 = 0 D = b² − 4ac = 1² − 4 ⋅ 1 ⋅ (−2) = 1 + 8 = 9 > 0 имеет 2 корня
x₁ = $$ =\frac{-b+\sqrt{D}}{2 a}=\frac{-1+\sqrt{9}}{2 ⋅ 1} $$ = −1 + 3/2 = 2/2 = 1 x₂ = $$ \frac{-b-\sqrt{D}}{2 a}=\frac{-1-\sqrt{9}}{2 ⋅ 1} $$ = −1 − 3/2 = −4/2 = −2
x₁ = 1, x₂ = −2
3) x² + х − 2/x + 3 = −5 ОДЗ: x + 3 ≠ 0, x ≠ −3 x² + х − 2/x + 3 = −5/1 x² + х − 2 = −5(x + 3) x² + х − 2 + 5x + 15 = 0 x² + 6x + 13 = 0 D = b² − 4ac = 6² − 4 ⋅ 1 ⋅ 13 = 36 − 52 = −16 < 0 не имеет корней