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If (\sqrt{5}=\frac{p}{q}) is assumed in lowest form and (p^2=5q^2) is obtained, in which form should (p) be written?यदि (\sqrt{5}=\frac{p}{q}) सरलतम रूप में माना जाए और (p^2=5q^2) मिले, तो (p) को किस रूप में लिखना उचित है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (p=5k)(p=5k)
Step 1: From (p^2=5q^2), (p^2) is divisible by (5). Step 2: Since (5) is prime, (p) is divisible by (5). Step 3: After divisibility, write (p=5k), where (k) is an integer.चरण 1: (p^2=5q^2) से (p^2) (5) से विभाज्य है। चरण 2: (5) अभाज्य है, इसलिए (p) (5) से विभाज्य है। चरण 3: विभाज्यता मिलने पर (p=5k) लिखें, जहां (k) पूर्णांक है।
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