Find all real solutions to the equation 2^x+3^x+6^x=x^2. Romania 1990

This video explains how to find all real solutions to the equation 2^x+3^x+6^x=x^2. Firstly, we show that the equation has a unique solution for x is less than or equal to zero and find the solution using the bisection method. Secondly, we show that the equation has no solutions for x greater than zero.

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Nice method. For the case x>0, alternatively, it can be shown that f’(x)>0.