Question

giải phương trình:

|x-2|+|x-3|=15

Answer 1

TH1: \(x\le2\) <=> \(\left\{{}\begin{matrix}\left|x-2\right|=2-x\\\left|x-3\right|=3-x\end{matrix}\right.\)

PT <=> 2-x + 3-x = 15

<=> x = -5 (chọn)

TH2: \(2< x< 3< =>\left\{{}\begin{matrix}\left|x-2\right|=x-2\\\left|x-3\right|=3-x\end{matrix}\right.\)

PT <=> x-2 + 3-x = 15

<=> x = \(\varnothing\)

TH3: \(x\ge3\) <=> \(\left\{{}\begin{matrix}\left|x-2\right|=x-2\\\left|x-3\right|=x-3\end{matrix}\right.\)

PT <=> x-2 + x-3 = 15

<=> x = 10 (chọn)

KL: \(S\in\left\{-5;10\right\}\)