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On (\mathbb{R}), (a*b=a+b+mab). If the inverse of (2) is (-1), what is the value of (m)?समुच्चय (\mathbb{R}) पर (a*b=a+b+mab) है। यदि (2) का प्रतिलोम (-1) है, तो (m) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{1}{2})(\frac{1}{2})
Step 1: The identity for this operation is (0). Step 2: If (2) and (-1) are inverses, then (2*(-1)=0). Step 3: (2-1-2m=0) gives (1-2m=0), so (m=\frac{1}{2}).चरण 1: इस क्रिया का तत्समक (0) है। चरण 2: (2) और (-1) प्रतिलोम हैं, इसलिए (2*(-1)=0)। चरण 3: (2-1-2m=0) से (1-2m=0), अतः (m=\frac{1}{2})।
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