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How do we solve a equation such as $$|x^2-4x+3|=x^2-4x+3$$

What are the most necessary steps to written,when solving such a question in a pure mathematics paper?

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    For $a\in \mathbb{R}$, note that $|a|=a$ if and only if $a\geq 0$. – 2017-01-11

1 Answers 1

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Using $|x| = x\;,$ when $x\geq 0$

So $|x^2-4x+3| = x^2-4x+3\Rightarrow x^2-4x+3\geq 0$

So $(x-1)(x-3)\geq 0$

So $x\leq 1\cup x\geq 3$

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    And can we solve a equation such as | x-3 | > |2x-4 | by taking (x-3)^2 > (2x-4)^2 – 2017-01-11
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    yes you can solve it – 2017-01-11