Let's assume we have two real numbers, a and b, such that a + b = 1.
Step 1: Square the larger number and add the smaller number:
If a > b, then by squaring a, we get a^2, and by adding b, we have a^2 + b.
Step 2: Square the smaller number and add the larger number:
If b > a, then by squaring b, we get b^2, and by adding a, we have b^2 + a.
What will be true?
In general, without any specific information about the values of a and b, it is not possible to determine whether a^2 + b or b^2 + a will be greater. The result will depend on the actual values of a and b.
For example, if a = 0.5 and b = 0.5, then both a^2 + b and b^2 + a will be equal to 0.75.
If a = 0.2 and b = 0.8, then a^2 + b = 0.24 and b^2 + a = 0.84.
If a = -1 and b = 2, then a^2 + b = 3 and b^2 + a = 5.
So, without more specific information, we cannot determine a general rule for which expression will be greater.