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If (x=\sqrt{2}+\sqrt{3}) then what is the correct conclusion about (x)?यदि (x=\sqrt{2}+\sqrt{3}) है तो (x) के बारे में सही निष्कर्ष क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (x) is irrational(x) अपरिमेय है
Step 1: Suppose (\sqrt{2}+\sqrt{3}) is rational. Step 2: Squaring gives (5+2\sqrt{6}) so (\sqrt{6}) would be rational which is false. Step 3: Do not decide the sum of two different irrational numbers without reasoning.चरण 1: मान लें (\sqrt{2}+\sqrt{3}) परिमेय है। चरण 2: वर्ग करने पर (5+2\sqrt{6}) परिमेय होना चाहिए इसलिए (\sqrt{6}) परिमेय मिलेगा जो गलत है। चरण 3: दो अलग अपरिमेय संख्याओं के योग को सीधे परिमेय या अपरिमेय न मानें।
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