Tìm x, biết: a) x^2 -25 = 3x -15 b) (x-1)^3 +3(x+1)^2 = (x^2 -2x

* Hướng dẫn giải

a)

$\begin{array}{l}{x}^2–25=3x–15\\ \left(x^2–25\right)-\left(3x–15\right)=0\\ \left(x-5\right)\left(x+5\right)-3\left(x-5\right)=0\\ \left(x-5\right)\left(x+5-3\right)=0\\ \left(x-5\right)\left(x+2\right)=0\\ \Rightarrow \left[\begin{array}{l}x-5=0\\ x+2=0\end{array}\right.\\ \Rightarrow \left[\begin{array}{l}x=5\\ x=-2\end{array}\right.\end{array}$

Vậy $x\in \left\{-2;5\right\}$

b)

$\begin{array}{l}{\left(x–1\right)}^3+3{\left(x+1\right)}^2=\left(x^2–2x+4\right)\left(x+2\right)\\ \left(x^3-3x^2+3x-1\right)+3\left(x^2+2x+1\right)=x^3+8\\ x^3-3x^2+3x-1+3x^2+6x+3=x^3+8\\ 9x+2=8\\ 9x=6\\ x=\frac{2}{3}\end{array}$

Vậy $x=\frac{2}{3}$