Question

Розв'язати систему рiвнянь
{3y²-xy = -1,
{x+3y= 5

Answer 1

$3 {y}^{2} - xy = - 1 \ x + 3y = 5 \ \3y {}^{2} - y(5 - 3y) = - 1 \ x = 5 - 3y \ \ 3y {}^{2} - y(5 - 3y) = - 1 \ 3 {y}^{2} - 5y + 3 {y}^{2} = - 1 \ 6 {y}^{2} - 5y + 1 = 0 \ D = ( - 5) {}^{2} - 4 times 6 times 1 = 25 - 24 = 1 : : : (1) \ y {1} = frac{5 + 1}{12} = frac{6}{12} = frac{1}{2} = 0.5 \ y{2} = frac{5 - 1}{12} = frac{4}{12} = frac{1}{3} \ \ x{1} = 5 - 3 times 0.5 = 5 - 1.5 = 3.5 \ x{2} = 5 - 3 times frac{1}{3} = 5 - 1 = 4 \ \ Ответ: : (3.5 : ; : 0.5) : ; : (4 : ; : frac{1}{3} )$