Question

If a^2=b^2, does a=b? Explain and justify your answer.

Answer 1

not necessarily

Explanation:

Taking the square root of both sides, you have ...

±a = ±b

Those four cases resolve to two unique cases:

a = ±b

The given equation will be true if a = b or if a = -b. If a and b are constrained to have the same sign, then a=b is the only solution.