Question

Решите уравнение: x^2-15x+13+(2/x^2-15x+16)=0 Срочно

Answer 1

$x^2-15x+13+ \frac{2}{x^2-15x+16}=0$
Область определения x^2 - 15x + 16 ≠ 0

Замена x^2 - 15x + 16 = y
y - 3 + 2/y = 0
Умножаем все на y
y^2 - 3y + 2 = 0
(y - 1)(y - 2) = 0

y1 = x^2 - 15x + 16 = 1
x^2 - 15x + 15 = 0
D = 15^2 - 4*1*15 = 225 - 60 = 165
x1 = (15 - √165)/2; x2 = (15 + √165)/2

y2 = x^2 - 15x + 16 = 2
x^2 - 15x + 14 = 0
D = 15^2 - 4*1*14 = 225 - 56 = 169 = 13^2
x3 = (15 - 13)/2 = 1; x4 = (15 + 13)/2 = 14