The biquadratic equation. Equations reducible to quadratic ones
Answers are for parents and teachers.
1
Solve x⁴ - 17x² + 16 = 0.
x = ±1, x = ±4
2
Solve x⁴ - 4x² = 0.
x = 0, x = ±2
3
Solve x²/(x + 1) = 1/(x + 1).
x = 1
4
Solve x + 10/x = 7 (x ≠ 0).
x₁ = 2, x₂ = 5
5
Why does x⁴ + x² + 5 = 0 have no root?
Because x⁴ ≥ 0 and x² ≥ 0, so the left side is at least 5 > 0.