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In the operation (a\ast b=2ab), (\frac{1}{2}) is the identity. What is the inverse of (4)?क्रिया (a\ast b=2ab) में (\frac{1}{2}) तत्समक है। (4) का प्रतिलोम क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{1}{8})(\frac{1}{8})
Step 1: For inverse (x), (4\ast x=\frac{1}{2}) must hold. Step 2: (2\cdot4\cdot x=\frac{1}{2}), so (8x=\frac{1}{2}), giving (x=\frac{1}{16}). Step 3: Solve fractional equations slowly to avoid calculation errors.चरण 1: प्रतिलोम (x) के लिए (4\ast x=\frac{1}{2}) होना चाहिए। चरण 2: (2\cdot4\cdot x=\frac{1}{2}), इसलिए (8x=\frac{1}{2}) और (x=\frac{1}{16}) नहीं, ध्यान से (x=\frac{1}{16}) आता है। चरण 3: भिन्नों में गुणा करते समय समीकरण को धीरे हल करें।
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