यदि (x) अपरिमेय है और \(x+ \sqrt{2}\) परिमेय है, तो (x) का संभावित रूप कौन-सा हो सकता है?
If (x) is irrational and \(x+\sqrt{2}\) is rational, which can be a possible form of (x)?
Explanation opens after your attempt
Correct Answer
A. \(3-\sqrt{2}\)
Concept
To make \(x+\sqrt{2}\) rational, (x) should contain a \(-\sqrt{2}\) part.
Why this answer is correct
If \(x=3-\sqrt{2}\), then \(x+\sqrt{2}=3\), which is rational.
Exam Tip
Look for cancellation of the irrational part. चरण 1: \(x+\sqrt{2}\) को परिमेय बनाने के लिए (x) में \(-\sqrt{2}\) वाला भाग होना चाहिए। चरण 2: \(x=3-\sqrt{2}\) रखने पर \(x+\sqrt{2}=3\), जो परिमेय है। चरण 3: अपरिमेय भाग के कटने की संभावना खोजें।
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