Question

Решите уравнения: 1) (7х-5)х=(1,5-2.1х) 2) (1-8х)х=(11,2х-1,4) 3) (1,7х-1/3)х=(3-15,3х)*1/2 4) (х/7-1 6/7)х=(3,9-0,3х)*1/35

Answer 1

1) (7х-5)х=(1,5-2.1х); 7х²-5х = 1,5 - 2.1х| · 10; 70х²- 50х = 15 - 21х; 70х²- 29х - 15 = 0;

D = 29² + 4·70·15 = 841 + 4200 = 5041; √D = 71; x₁ = (29 + 71)/140 = 100/140=5/7;

x₂ = (29 - 71)/140 = 42/140=3/20 = 0.15. ответ: 5/7; 0,15.

2) (1 - 8х)х=(11,2х - 1,4); x - 8х² = 11,2х - 1,4|·5; 5x - 40х² = 56х - 7; 40х² + 51x - 7 = 0; D = 51² + 1120 = 2601 + 1120 = 3721; √D = 61; x₁ = (-51 + 61)/80 = 10/80= 1/8 = 0,125; x₂ = (-51 - 61)/80 = -111/80= -1,3785. ответ: 0,125; -1,3785.

3) (1,7х - 1/3)х=(3 - 15,3х)*1/2; 1,7х² - (1/3)х = (3 - 15,3х)*1/2|·60; 102х² -20х = (30 - 153х)*3; 102х² -20х = 90 - 459х; 102х² +439х - 90 = 0; D = 439² + 360·102 = 229441; √D = 479; x₁ = (-439+ 479)/204 = 40/204 = 10/51; x₂ =(-439 - 479)/204 = -918/204 = -459/102 = -153/34 = -9/2 = -4,5. ответ: 10/51; -4,5.

4) (х/7 - 1(6/7))х=(3,9-0,3х)*1/35|·350; 50x² - 650x = 39 - 3x; 50x² - 647x - 39 = 0; D = 418609 + 200·39 = 426409; √D = 653; x₁ = (650 + 653)/100 = 13,03; x₂ = (650 - 653)/100 = - 0,03. ответ: 13,03; - 0,03.