Question

Найдите корни уравнения(подробно) :


$\frac{x^{2} }{3} - \frac{7x}{18} + 4 = 5 \frac{1}{9}$

Answer 1

$\frac{x^{2} }{3} - \frac{7x}{18} + 4 = 5 \frac{1}{9} \\ 6 {x}^{2} - 7x + 72 = 92 \\ 6 {x}^{2} - 7x - 20 = 0 \\ d = 49 + 480 = 529 = {23}^{2} \\ x1 = \frac{7 + 23}{12} = \frac{30}{12} = 2.5 \\ x2 = \frac{7 - 23}{12} = \frac{ - 16}{12} = - \frac{4}{3} = - 1 \frac{1}{3}$

Answer 2

$\frac{x^2}{3}-\frac{7x}{18}+4=5\frac{1}{9}\\\\\frac{x^2}{3}-\frac{7x}{18}+4=\frac{46}{9}$

Умножаем обе части уравнения на 18.

$\frac{18*x^2}{3}-\frac{18*7x}{18}+18*4=\frac{18*46}{9}\\\\6x^2-7x+72=92\\\\6x^2-7x+72-92=0\\\\6x^2-7x-20=0\\\\\\D=b^2-4ac\\\\D=49-4*6*(-20)=49+480=529=23^2\\\\x_1=\frac{7-23}{12}=-\frac{16}{12}=-1\frac{1}{3}\\\\x_2=\frac{7+23}{12}=\frac{30}{12}=2\frac{1}{2}=2,5$

Ответ: {- 1 ¹/₃ ;  2,5}