X has two values -1 and 1. But if we use geometric mean=sqrt(ab)=x, we get only x=1. Why does this formula give only one solution?
You are mistaken about the square root function. For any positive number, a, there exist two numbers, x, such that . However, the square root is defined as the positive one. That is , , , etc.. -1, -2, -3 are NOT square roots.
(The reason we write the in "if then " is because the does NOT include both.)