1. 1) x(2x + 3) - 8 = 2x^2 + 11x
2x^2 + 3x - 8 = 2x^2 + 11x
-8 = 11x - 3x = 8x
x = -1
2) 7x - (3x-1)^2 = 10 - (3x-1)(3x+1)
7x - (9x^2 - 6x + 1) = 10 - (9x^2 - 1)
7x - 9x^2 + 6x - 1 = 10 - 9x^2 + 1
7x + 6x = 10 + 1 + 1
13x = 12
x = 12/13
3) x + (x + 10)/5 = (x - 2)/3
Умножаем все на 15
15x + 3(x + 10) = 5(x - 2)
15x + 3x + 30 = 5x - 10
18x - 5x = -10 - 30
13x = -40
x = -40/13
4) (2x - 0,5)/3 + (x - 2)/40 = 0,5
Умножаем все на 120
40(2x - 0,5) + 3(x - 2) = 60
80x - 20 + 3x - 6 = 60
83x = 60 + 20 + 3 = 86
x = 86/83
5) 3*(2/4)*x - (10x - 7)/12 = 2,5x
3x/2 - (10x - 7)/12 = 2,5x
Умножаем все на 12
3x*6 - (10x - 7) = 2,5x*12
8x + 7 = 30x
7 = 30x - 8x = 22x
x = 7/22
2. 1) 2x^2 + 9x + 4 = 0
D = 9^2 - 4*2*4 = 81 - 32 = 49 = 7^2
x1 = (-9 - 7)/4 = -16/4 = -4; x2 = (-9 + 7)/4 = -2/4 = -1/2
2) 19x^2 - 76 = 0
x^2 = 76/19 = 4
x1 = -2; x2 = 2
3) (1/6)*x^2 - (13/6)*x + 7 = 0
Умножаем все на 6
x^2 - 13x + 42 = 0
D = 13^2 - 4*1*42 = 169 - 168 = 1 = 1^2
x1 = (13 - 1)/2 = 12/2 = 6; x2 = (13 + 1)/2 = 14/2 = 7
4) (2/3)*x^2 - (3/2)*x = 0
Умножаем все на 6
4x^2 - 9x = 0
x(4x - 9) = 0
x1 = 0; x2 = 9/4
x(x+1)-12=х²+х-12
х²+х-12≡х²+х-12
Получили левая часть тождественно равна правой, что и требовалось доказать.