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How to solve:|x²-4x+3| = -|x²-5x+4|I am not understanding whether this question will have no solution or if it will have a solution how do I open a mod with a minus sign info of it????

Answer»

Here we go,

| {x}^{2} - 4x + 3 | = - | {x}^{2} - 5x + 4 | \\ \frac{| {x}^{2} - 3x - x + 3 |}{| {x}^{2} - 4x - x + 4|} = - 1 \\ \frac{| x(x - 3) - (x -3 )|}{|x(x - 4) - (x - 4)| } = - 1 \\ \frac{| (x - 1)(x - 3)|}{|(x - 1)(x - 4) |} = - 1 \\ \frac{| x - 3|}{|x - 4 |} = - 1 \\ | \frac{x - 3}{x - 4} | = - 1
You can SEE that it's giving a negative value which is not what happens when you USE mod on all of RHS,

If you're still not satisfies use wave curvy method to get the range and you're gonna FIND there is none.
So no SOLUTIONS.


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