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Which statement is a wrong step in the proof of irrationality of (\sqrt{2})?कौन सा कथन (\sqrt{2}) की अपरिमेयता के प्रमाण में गलत कदम है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: From (p^2=2q^2), directly (p=2q)(p^2=2q^2) से सीधे (p=2q)
Step 1: From (p^2=2q^2), we conclude (p^2) is even. Step 2: This gives (p) even, but not directly (p=2q). Step 3: The correct form is (p=2r), where (r) is an integer.चरण 1: (p^2=2q^2) से (p^2) के सम होने का निष्कर्ष निकलता है। चरण 2: इससे (p) सम है, लेकिन सीधे (p=2q) नहीं लिख सकते। चरण 3: सही रूप (p=2r) होता है, जहां (r) पूर्णांक है।
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