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If (r) is a prime number and (\sqrt{r}=\frac{p}{q}) is assumed in lowest form, what is the first general conclusion from (p^2=rq^2)?यदि (r) एक अभाज्य संख्या है और (\sqrt{r}=\frac{p}{q}) सरलतम रूप में माना जाए, तो (p^2=rq^2) से कौन-सा पहला सामान्य निष्कर्ष निकलेगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (r\mid p)(r\mid p)
Step 1: From (p^2=rq^2), we get (r\mid p^2). Step 2: Since (r) is prime, (r\mid p). Step 3: After this, put (p=rk) to show (r\mid q).चरण 1: (p^2=rq^2) से (r\mid p^2) मिलता है। चरण 2: (r) अभाज्य है, इसलिए (r\mid p) होगा। चरण 3: इसके बाद (p=rk) रखकर (r\mid q) दिखाया जाता है।
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