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墨滴

Opsimath

2021/09/17  阅读:29  主题:默认主题

STEP 5

The question today comes from 1997 Paper I. The original question is shown below.

Find all the solutions of the equation

A (somewhat boring) question that looks more difficult than it is. You have to deal with the discontinuous modulus function, and there is no clever way of doing it. The only possible approach is considering different cases.

Solution. Consider the critical points. I will leave the simplifications to the readers.

Let .

If , only if which is a solution.

If , so no solutions.

If , only if which is not a solution.

If , only if which is a solution.

If , so the equation is satisfied for all .

Thus, or .

Extension. Draw the graph of . Also refer to 1999 STEP 1 q. 4 and 2014 STEP 2 q. 7.

Opsimath

2021/09/17  阅读:29  主题:默认主题

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Opsimath