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Ravi claims that \(x=\frac{3+\sqrt{2}}{5}\) is rational because its denominator is 5. What is the error in Ravi’s claim?रवि का दावा है कि \(x=\frac{3+\sqrt{2}}{5}\) परिमेय है, क्योंकि इसका हर 5 है। रवि के दावे में कौन-सी त्रुटि है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Dividing an irrational number by a non-zero rational number gives an irrational resultशून्येतर परिमेय संख्या से अपरिमेय संख्या को भाग देने पर परिणाम अपरिमेय रहता है
\(3+\sqrt{2}\) is irrational. Dividing it by the non-zero rational number 5 keeps the result irrational. Exam tip: if \(x\) were rational, then \(5x-3=\sqrt{2}\) would be rational, which is a contradiction.\(3+\sqrt{2}\) अपरिमेय है। इसे 5 जैसी शून्येतर परिमेय संख्या से भाग देने पर परिणाम अपरिमेय ही रहता है। परीक्षा टिप: यदि \(x\) परिमेय मानें, तो \(5x-3=\sqrt{2}\) परिमेय होगा, जो विरोधाभास है।
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