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Post #694
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➕M ➕Math Lab ➕
@math
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The equation 𝑥²=1 has two solutions.
They are 𝑥 = 1 and 𝑥 = -1.
We can see that if you substitute 1 in as 𝑥, 1² = 1. If instead you substitute -1 as 𝑥, (-1)² = (-1)*(-1) = 1.
In general, 𝑥² = a, where a is a positive real number, has solutions 𝑥 = √a and 𝑥 = -√a.
If a is not a positive number, or is not a real number, but rather a complex number, then we need to expand our horizons.
There will still be two answers, as with the positive number case.
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They are 𝑥 = 1 and 𝑥 = -1.
We can see that if you substitute 1 in as 𝑥, 1² = 1. If instead you substitute -1 as 𝑥, (-1)² = (-1)*(-1) = 1.
In general, 𝑥² = a, where a is a positive real number, has solutions 𝑥 = √a and 𝑥 = -√a.
If a is not a positive number, or is not a real number, but rather a complex number, then we need to expand our horizons.
There will still be two answers, as with the positive number case.
✅ Follow @math
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