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Which of the following expressions can be rational for an irrational number \(x\)?निम्नलिखित में से कौन-सा व्यंजक किसी अपरिमेय संख्या \(x\) के लिए परिमेय हो सकता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x^2\)\(x^2\)
Take \(x=\sqrt{2}\). It is irrational, but \(x^2=2\) is rational. If \(x+1\), \(2x\), or \(1/x\) were rational, then \(x\) would also be rational, a contradiction. Exam tip: test a claim using a counterexample.\(x=\sqrt{2}\) लेने पर \(x\) अपरिमेय है, लेकिन \(x^2=2\) परिमेय है। \(x+1\), \(2x\) या \(1/x\) परिमेय होने पर \(x\) परिमेय हो जाएगा, जो विरोधाभास है। परीक्षा टिप: प्रतिउदाहरण खोजें।
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