Question

Решите уравнения с помощью нахождения дискриминанта
26) 2х2-30х+52=0

27) -х2+11х-18=0

28) х2-9х+8=0

29) 0,5х2-3,5х+5=0

Answer 1

26)

$2 {x}^{2} - 30x + 52 = 0 \\ d = ( - 30)^{2} - 4 \times 2 \times 52 = 900 - 416 = 484 = {22}^{2} \\ x1 = \frac{30 - 22}{2 \times 2} = \frac{8}{4} = 2 \\ x2 = \frac{30 + 22}{2 \times 2} = \frac{52}{4} = 13$

27)

$- {x}^{2} + 11x - 18 = 0( \times - 1) \\ {x}^{2} - 11x + 18 = 0 \\ d = ( - 11)^{2} - 4 \times 1 \times 18 = 121 - 72 = 49 = {7}^{2} \\ x1 = \frac{11 - 7}{2} = \frac{4}{2} = 2 \\ x2 = \frac{11 + 7}{2} = \frac{18}{2} = 9$

28)

${x}^{2} - 9x - 18 = 0 \\ d = ( - 9) ^{2} - 4 \times 1 \times ( - 18) = 81 + 72 = 153 = \sqrt{153} \\ x1 = \frac{9 + \sqrt{153} }{2} = \frac{9 + 3 \sqrt{17} }{2} \\ x2 = \frac{9 - \sqrt{153} }{2} = \frac{9 - 3 \sqrt{17} }{2}$

29)

$0.5 {x}^{2} - 3.5x + 5 = 0 \\ d = ( - 3.5)^{2} - 4 \times 0.5 \times 5 =12.25 - 10 = 2.25 = {1.5}^{2} \\ x1 = \frac{3.5 + 1.5}{2 \times 0.5} = \frac{5}{1} = 5 \\ x2 = \frac{3.5 - 1.5}{2 \times 0.5} = 2$

d - дискриминант