Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 632

а) 2x − 5/x + 5 − 4 = 0 ОДЗ: x + 5 ≠ 0, x ≠ −5 2x − 5/x + 5 = 4 2x − 5/x + 5 = 4/1 2x − 5 = 4(x + 5) 2x − 5 = 4x + 20 2x − 4x = 20 + 5 −2x = 25 x = 25 : (−2) x = −12,5
б) 12/7 − x = x ОДЗ: 7 − x ≠ 0, x ≠ 7 12/7 − x = x/1 (7 − x)x = 12 7x − x² − 12 = 0 −x² + 7x − 12 = 0 D = b² − 4ac = 7² − 4 ⋅ (−1) ⋅ (−12) = 49 − 48 = 1 > 0 имеет 2 корня
x₁ = $$ \frac{-b+\sqrt{D}}{2 a}=\frac{-7+\sqrt{1}}{2(-1)} $$ = −7 + 1/−2 = −6/−2 = 3 x₂ = $$ =\frac{-b-\sqrt{D}}{2 a}=\frac{-7-\sqrt{1}}{2(-1)} $$ = −7 − 1/−2 = −8/−2 = 4
x₁ = 3, x₂ = 4
в) x² − 4/4x = 3x − 2/2x ОДЗ: x ≠ 0 x² − 4/4x − (3x − 2) ⋅ 2/2x ⋅ 2 = 0 x² − 4 − 6x + 4/4x = 0 x² − 6x = 0 x(x − 6) = 0 x = 0 x − 6 = 0 x = 6
г) 10/2x − 3 = x − 1 ОДЗ: 2x − 3 ≠ 0, x ≠ 1,5 10/2x − 3 = x − 1/1 (2x − 3)(x − 1) = 10 2x² − 2x − 3x + 3 − 10 = 0 2x² − 5x − 7 = 0 D = b² − 4ac = (−5)² − 4 ⋅ 2 ⋅ (−7) = 25 + 56 = 81 > 0 имеет 2 корня
x₁ = $$ \frac{-b+\sqrt{D}}{2 a}=\frac{5+\sqrt{81}}{2 ⋅ 2} $$ = 5 + 9/4 = 14/4 = 7/2 = 3,5 x₂ = $$ \frac{-b-\sqrt{D}}{2 a}=\frac{5-\sqrt{81}}{2 ⋅ 2}= $$ = 5 − 9/4 = −4/4 = −1
x₁ = 3,5, x₂ = −1
д) 8/x = 3x + 2 ОДЗ: x ≠ 0 8/x = 3x + 2/1 x(3x + 2) = 8 D = b² - 4ac = 2² − 4 ⋅ 3 ⋅ (−8) = 4 + 96 = 100 > 0 имеет 2 корня
x₁ = $$ \frac{-b+\sqrt{D}}{2 a}=\frac{-2+\sqrt{100}}{2 ⋅ 3} $$ = −2 + 10/6 = 8/6 = 4/3 = 11/3 x₂ = $$ \frac{-b-\sqrt{D}}{2 a}=\frac{-2-\sqrt{100}}{2 ⋅ 3} $$ = −2 − 10/6 = −12/6 = −2 x₁ = 11/3, x₂ = −2
е) x² + 4x/x + 2 = 2x/3 ОДЗ: x + 2 ≠ 0, x ≠ −2 3(x² + 4x) = 2x(x + 2) 3x² + 12x = 2x² + 4x 3x² + 12x − 2x − 4x = 0 x² + 8x = 0 x(x + 8) = 0 x = 0 x + 8 = 0 x = −8
ж) 2x² − 5x + 3/10x − 5 = 0 ОДЗ: 10x − 5 ≠ 0, x ≠ 0,5 2x² − 5x + 3 = 0 D = b² − 4ac = (−5)² − 4 ⋅ 2 ⋅ 3 = 25 − 24 = 1 > 0 имеет 2 корня
x₁ = $$ \frac{-b+\sqrt{D}}{2 a}=\frac{5+\sqrt{1}}{2 ⋅ 2} $$ = 5 + 1/4 = 6/4 = 3/2 = 1,5 x₂ = $$ =\frac{-b-\sqrt{D}}{2 a}=\frac{5-\sqrt{1}}{2 ⋅ 2}= $$ = 5 − 1/4 = 4/4 = 1
x₁ = 1,5, x₂ = 1
з) 4x³ − 9x/x + 1,5 = 0 ОДЗ: x + 1,5 ≠ 0, x ≠ −1,5 4x³ − 9x = 0 x(4x² − 9) = 0 x(2x − 3)(2x + 3) = 0 x = 0 2x − 3 = 0,x = 1,5 2x + 3 = 0,x = −1,5 х = −1,5 не является корнем