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If (n) is odd, then (n^2) is odd. In which proof is this fact used directly?यदि (n) विषम है, तो (n^2) विषम होता है। यह तथ्य किस प्रमाण में सीधे प्रयोग होता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: In the irrationality of (\sqrt{2})(\sqrt{2}) की अपरिमेयता में
Step 1: In the proof for (\sqrt{2}), (p^2) is found even. Step 2: If (p) were odd, (p^2) would be odd, so (p) is even. Step 3: This parity rule is very useful for (\sqrt{2}).चरण 1: (\sqrt{2}) के प्रमाण में (p^2) सम मिलता है। चरण 2: यदि (p) विषम होता तो (p^2) विषम होता, इसलिए (p) सम है। चरण 3: सम-विषम का यह नियम (\sqrt{2}) में बहुत उपयोगी है।
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