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On (\mathbb{R}), (a*b=a+b+c). What will be the inverse of an element (p)?समुच्चय (\mathbb{R}) पर (a*b=a+b+c) है। किसी अवयव (p) का प्रतिलोम क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (-p-2c)(-p-2c)
Step 1: First find identity: (a+e+c=a), so (e=-c). Step 2: From (p*x=e), (p+x+c=-c). Step 3: Hence (x=-p-2c), the inverse of (p).चरण 1: पहले तत्समक (e) निकालें: (a+e+c=a), इसलिए (e=-c)। चरण 2: (p*x=e) से (p+x+c=-c)। चरण 3: इसलिए (x=-p-2c), यही (p) का प्रतिलोम है।
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