Tìm số tự nhiên x biết rằng: (x – 5)^4 = (x – 5)^6.

(x – 5)⁴ = (x – 5)⁶

⇔ (x – 5)⁴[(x – 5)² – 1] = 0

⇔ (x – 5)⁴ (x – 5 – 1)(x – 5 + 1) = 0

⇔ (x – 5)⁴(x – 6)(x – 4) = 0

⇔ \(\left[ \begin{array}{l}x - 5 = 0\\x - 6 = 0\\x - 4 = 0\end{array} \right.\)

⇔ \(\left[ \begin{array}{l}x = 5\\x = 6\\x = 4\end{array} \right.\)

Vậy x ∈{4; 5; 6}.