In the proof of (\sqrt{2}), if someone says that (p^2=2q^2) immediately makes both (p) and (q) even, what is the correct comment?
Answer and explanation
Correct answer: This is incomplete; first (p) is proved even and then (q) is proved even by substitution
Step 1: From (p^2=2q^2), first only (p^2) and then (p) are proved even. Step 2: After substituting (p=2k), (q^2=2k^2) is obtained and then (q) is proved even. Step 3: Skipping order is considered an error in proof writing.
Frequently asked questions
What is the correct answer to this question?
This is incomplete; first (p) is proved even and then (q) is proved even by substitution
Why is this the correct answer?
Step 1: From (p^2=2q^2), first only (p^2) and then (p) are proved even. Step 2: After substituting (p=2k), (q^2=2k^2) is obtained and then (q) is proved even. Step 3: Skipping order is considered an error in proof writing.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Proof of irrationality of √2, √3, √5.
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