I used a WolframAlpha query to solve a problem relevant to some applied work I'm doing. The input interpretation box shows that WolframAlpha has correctly understood my input.
Because I have the Pro version, WolframAlpha produces not only a solution and some conditions, but also the intermediate steps leading to an answer. I paste the full screenshot here, but below I've chopped out the intermediate steps for ease of viewing. The circled parts are drawn in by me, to help ask some questions about the output.
Are the yellow and green answers fundamentally the same, i.e. do they hold under the same conditions? I couldn't understand why WolframAlpha rendered two different-looking solutions for the same problem.
What do the conditions mean? Here is my current understanding, based on nothing more than what seems sensible to me based on the design of the webpage: if either the red box condition fails to hold, or the blue box condition fails to hold, then the solution is not valid.
The red box contains two separate elements. Iff both of them fail to hold, the red box has caused the overall solution to not be valid.
The blue box contains five separate elements. Iff all five of them fail to hold, then the blue box has caused the overall solution to not be valid.