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Define a New Calculation

Source: 1985 National High School Mathematics League, Exam One, Problem 10

February 24, 2020

Problem Statement

Define that x∗y=ax+by+cxyx*y=ax+by+cxy for all real numbers x,yx,y, where a,b,ca,b,c are uncertain. It is known that 1∗2=3,2∗3=41*2=3,2*3=4. If there exists a real number dd, for any real number xx, x∗d=xx*d=x, then d=d=________.
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