Решаем через дискриминант:
-x^2+5*x+43=0
a = -1; b = 5; c = 43
D = b^2 - 4*a*c
D = 5^2 - 4*(-1)*43 = 197 > 0
x = (-b+-D^1/2)/(2*a) (Пояснение: ^1/2 - корень)
x_1,2 = (-5+-197^1/2)/(2*(-1))
x_1 = (-5-197^1/2)/(-2)
x_2 = (-5+197^1/2)/(-2)
Сумма корней:
x_1+x_2 =
(-5-197^1/2)/(-2) + (-5+197^1/2)/(-2) = (-5-(197^1/2) -5+(197^1/2))/(-2) =
(-10) / (-2) = 5
1. x^{2} - 9x + 20 = 0
x1, 2 = ( 9 +- \sqrt{81 - 80} ) / 2; x1 = 4; x2 = 5
2. x^{2} - 9x = 0 ; x = 9
3. x^{2} - 9x + 20 = 12
x^{2} - 9x + 6 = 0
x1, 2 = ( 9 +- \sqrt{81 - 24} ) / 2; x1 \approx 0.73; x2 \approx 8.27
4. x^{2} - 9x - 10 = 0
x1, 2 = ( 9 +- \sqrt{81 + 40} ) / 2; x1 = 10; x2 = 5
Решаем по дискриминанту
А) D= 49-48= 1
X1= (7+1)/2=4
Х2= (7-1)/2=3
Ответ: 4 и 3
1)143-13x=234:9
143-13x=26
-13x=26-143
-13x=-117
x=-117:(-13)
x=9
2)5x-16=238:17
5x-16=14
5x=14+16
5x=30
x=6
3)21x-19=170
21x=170+19
21x=189
x=9