Question

Giải phương trình :

(x - 4,5 )³ - ( x -5,5 )³ = 12,25

Answer 1

\(\left(x-\frac{9}{2}\right)^3-\left(x-\frac{11}{2}\right)^3=\frac{49}{4}\)

\(\Leftrightarrow\left(2x-9\right)^3-\left(2x-11\right)^3=98\)

\(\Leftrightarrow\left(2x-9\right)^3+27=\left(2x-11\right)^3+125\)

\(\Leftrightarrow\left(2x-6\right)\left(4x^2-42x+117\right)=\left(2x-6\right)\left(4x^2-54x+201\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-6=0\\4x^2-42x+117=4x^2-54x+201\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\12x=84\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=3\\x=7\end{matrix}\right.\)