The wavelength order for different types of electromagnetic waves from shortest to longest is as follows:
1. **Gamma rays** (λ1) have the shortest wavelength.
2. **X-rays** (λ2) have a slightly longer wavelength than gamma rays.
3. **Infrared waves** (λ3) have a longer wavelength than X-rays.
4. **Microwaves** (λ4) have the longest wavelength among these options.
Therefore, the ascending order of wavelength is:
λ1 < λ2 < λ3 < λ4.
Answer: λ1 < λ2 < λ3 < λ4
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: