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On (\mathbb{R}), the operation (a*b=a+b-2ab) is defined. What is the inverse of (3)?समुच्चय (\mathbb{R}) पर संक्रिया (a*b=a+b-2ab) है। (3) का प्रतिलोम क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{3}{5})(\frac{3}{5})
Step 1: First find the identity. From (a+e-2ae=a), we get (e=0). Step 2: For inverse (x) of (3), (3+x-6x=0), so (3-5x=0). Step 3: Hence (x=\frac{3}{5}); while finding inverse, equate the result to the identity.चरण 1: पहले तत्समक निकालें। (a+e-2ae=a) से (e=0) मिलता है। चरण 2: (3) के प्रतिलोम (x) के लिए (3+x-6x=0), इसलिए (3-5x=0)। चरण 3: अतः (x=\frac{3}{5}); प्रतिलोम निकालते समय परिणाम को तत्समक के बराबर रखें।
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