7 (x+1/x) - x^2 (x^2+1/x^2) = 9

7 (x + 1/x) - 2 (x² + 1/x²) = 9,

x + 1/x = а,

(x + 1/x) ² = а²,

x² + 2 * х * 1/x + 1/x² = а²,

x² + 2 + 1/x² = а²,

x² + 1/x² = а² - 2,

7 а - 2 (а² - 2) = 9,

7 а - 2 а² + 4 = 9,

- 2 а² + 7 а + 4 - 9 = 0,

2 а² - 7 а + 5 = 0,

D = 49 - 4 * 2 * 5 = 9,

а₁ = (7 + 3) / (2 * 2) = 2, 5.

а₂ = (7 - 3) / (2 * 2) = 1.

x + 1/x = 2, 5,

x² + 1 = 2, 5 х,

x² - 2, 5 х + 1 = 0,

D = 6, 25 - 4 = 2, 25,

х₁ = (2, 5 + 1, 5) / 2 = 4/2 = 2.

х₂ = (2, 5 - 1, 5) / 2 = 1/2.

x + 1/x = 1.

x² - х + 1 = 0,

D = 1 - 4 < 0. Нет корней.