<em>Подставляем в первое уравнение системы, получившееся y.</em>
А)
x(x+2)(x+4)(x+6) = - 7
x(x+6) * (x+2)(x+4) =-7
(x² + 6x) * (x² +4x + 2x + 8) = - 7
(x² + 6x)(x² +6x + 8) = - 7
Замена x² + 6x = n
n (n + 8) = - 7
n² + 8n + 7 =0
D = 8² - 4*1*7 = 64 - 28 = 36 = 6² ; D>0
n₁ = ( - 8 - 6)/(2*1) = -14/2 = -7
n₂ = ( - 8 + 6)/(2*1) = - 2/2 = - 1
x² + 6x = -7
x² + 6x + 7 = 0
D = 6² - 4*1*7 = 36 - 28 = 8 = (2√2)² ; D>0
x₁ = (-6 -2√2)/(2*1) = -2(3 +√2)/2 = - (3+√2)
x₂ = (- 6 +2√2)/(2*1) = 2(-3 +√2)/2 = - 3 +√2
x² + 6x = -1
x² + 6x + 1 =0
D = 6² - 4*1*1 = 36 - 4 = 32 = (4√2)² ; D>0
x₁= (-6 - 4√2)/ (2*1) = -2(3+2√2)/2 = - (3+2√2)
x₂ = ( - 6 +4√2)/(2*1) = 2(-3+2√2)/2 = -3 +2√2
ответ: х₁ = - (3 + 2√2) ; х₂ = -(3 +√2) ; х₃ =-3+√2 ; х₄=- 3 + 2√2
б)
(х-3)(х-4)(х-5)(х-6) =3
(x-3)(x-6) *(x-4)(x-5) = 3
(x² - 6x -3x +18)(x² - 5x -4x + 20) = 3
(x² - 9x + 18)(x² - 9x + 20) = 3
Замена x² - 9x = k
(k + 18)(k + 20) = 3
k² + 20k + 18k + 360 - 3 = 0
k² + 38k + 357 = 0
D = 38² - 4*1*357 = 1444 - 1428 = 16 = 4² ; D>0
k₁ = (- 38 - 4) /(2*1) = - 42/2 = - 21
k₂ = (-38 + 4)/(2*1) = -34/2 = -17
x² - 9x = - 21
x² - 9x + 21 = 0
D = (-9)² - 4*1*21 = 81 - 84 = - 3 ; D<0 нет корней
х² - 9х = - 17
х² - 9х + 17 = 0
D = (-9)² - 4*1*17 = 81 - 68 = 13 = (√13)² ; D>0
x₁ = (9 - √13)/(2*1) = 0,5(9 - √13) = 4,5 - 0,5√13
x₂ = (9 + √13)/ (2*1) = 0,5(9 +√13) = 4,5 +0,5√13
ответ : х₁ = 4,5 - 0,5√13 ; х₂ = 4,5 + 0,5√13
2(3x-7)-5x<=3x-11
6x-14-5x<=3x-11
6x-5x-3x<=14-11
-2x<=3 | (-2)
x>=-1,5
Ответ: x>=-1,5
-2х - 12 = 6
-2х = 6+12
-2х = 18
Х = 18 : (-2)
Х = - 9
