The following proof aims to establish that -4 = 0 - HSC - SSCE Mathematics Extension 2 - Question 2 - 2022 - Paper 1
Question 2
The following proof aims to establish that -4 = 0.
Let a = -4
⇒ a² = 16 and 4a + 4 = -12
⇒ a² + 4a + 4 = 4
⇒ (a + 2)² = 2²
⇒ a + 2 = 2
⇒ a = 0
At wh... show full transcript
Worked Solution & Example Answer:The following proof aims to establish that -4 = 0 - HSC - SSCE Mathematics Extension 2 - Question 2 - 2022 - Paper 1
Step 1
Line 1
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Answer
In Line 1, the assertion made is that If we let a=−4, then it follows that this is a valid assignment. There is no implication error here because defining a variable is simply a statement.
Step 2
Line 2
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Answer
In Line 2, it states that a2=16 and 4a+4=−12. This is also a valid evaluation; however, we need to ensure that 4(−4)+4 equates to −12. Confirming this, we get −16+4=−12, hence it is correct.
Step 3
Line 3
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Answer
In Line 3, a2+4a+4=4 is rewritten correctly as (a+2)2=22. This is factually accurate; however, from our equivalence, it should result in a false statement given our prior definitions. Thus, this line is correctly derived but problematic based on prior definitions.
Step 4
Line 4
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Answer
In Line 4, a+2=2 implies a=0. This conclusion is incorrect because we initially assumed a=−4. Therefore, the error occurs at this line, making Line 4 the incorrect implication.
