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Functional nice equation and 0

Source: Bangladesh National MO 2013

March 5, 2019
algebrafunctionfunctional equation

Problem Statement

Higher Secondary P2
Let gg be a function from the set of ordered pairs of real numbers to the same set such that g(x,y)=āˆ’g(y,x)g(x, y)=-g(y, x) for all real numbers xx and yy. Find a real number rr such that g(x,x)=rg(x, x)=r for all real numbers xx.
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