Page 2.2: Avoiding Common Pitfalls
For each statement below, determine if they are true or false.
1) \( (a+b)^2 = a^2 + b^2 \)
2) \( \sqrt{a+b} = \sqrt{a} + \sqrt{b} \)
3) \( \sqrt{a^2 +b^2} = a + b \)
4) \( \frac{1}{a} + \frac{1}{b} = \frac{1}{a+b} \)
5) \( \frac{a+b}{a} = b \)
6) \( a^{-1} + b^{-1} = (a+b)^{-1} \)
- Answer
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Each statement above is false! Be careful from this point onwards. Whenever we write down a formula or we perform some sort of simplification, we should always take a moment and ask ourselves if the rule we are using is true! Many statements in math might look true but are not, as seen in the above example.