9. 1) x²-9=0; 2) 16-x²=0; 3) 25-4x²=0; 4) 49x²-16=0.

Решение:

1. \( x^2 - 9 = 0 \Rightarrow x^2 = 9 \Rightarrow x = \pm \sqrt{9} \Rightarrow x = \pm 3 \)
2. \( 16 - x^2 = 0 \Rightarrow x^2 = 16 \Rightarrow x = \pm \sqrt{16} \Rightarrow x = \pm 4 \)
3. \( 25 - 4x^2 = 0 \Rightarrow 4x^2 = 25 \Rightarrow x^2 = \frac{25}{4} \Rightarrow x = \pm \sqrt{\frac{25}{4}} \Rightarrow x = \pm \frac{5}{2} \)
4. \( 49x^2 - 16 = 0 \Rightarrow 49x^2 = 16 \Rightarrow x^2 = \frac{16}{49} \Rightarrow x = \pm \sqrt{\frac{16}{49}} \Rightarrow x = \pm \frac{4}{7} \)

Ответ: 1) \( x = \pm 3 \); 2) \( x = \pm 4 \); 3) \( x = \pm \frac{5}{2} \); 4) \( x = \pm \frac{4}{7} \).