Question

|1/3 + 2024x| + |2/3 + 2025x| = 4050x

help với

Answer 1

Do \(\left|\dfrac{1}{3}+2024x\right|+\left|\dfrac{2}{3}+2025x\right|\ge0;\forall x\)

\(\Rightarrow4050x\ge0\)

\(\Rightarrow x\ge0\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{1}{3}+2024x>0\\\dfrac{2}{3}+2025x>0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\left|\dfrac{1}{3}+2024x\right|=\dfrac{1}{3}+2024x\\\left|\dfrac{2}{3}+2025x\right|=\dfrac{2}{3}+2025x\end{matrix}\right.\)

Phương trình trở thành:

\(\dfrac{1}{3}+2024x+\dfrac{2}{3}+2025x=4050x\)

\(\Leftrightarrow1+4049x=4050x\)

\(\Leftrightarrow1=4050x-4049\)

\(\Leftrightarrow x=1\) (thỏa mãn)