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If (x=\sqrt{3}-\sqrt{2}) then which statement about (x) is correct?यदि (x=\sqrt{3}-\sqrt{2}) है तो (x) के बारे में सही कथन कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (x) is irrational(x) अपरिमेय है
Step 1: Suppose (\sqrt{3}-\sqrt{2}) is rational. Step 2: Squaring gives (5-2\sqrt{6}), forcing (\sqrt{6}) to be rational which is false. Step 3: The difference of unlike radicals is not directly an integer.चरण 1: मान लें (\sqrt{3}-\sqrt{2}) परिमेय है। चरण 2: वर्ग करने पर (5-2\sqrt{6}) से (\sqrt{6}) परिमेय होना पड़ेगा जो गलत है। चरण 3: अलग-अलग वर्गमूलों का अंतर सीधे पूर्णांक नहीं माना जाता।
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