Question

Giúp mình câu 10 với ạ

Answer 1

Câu 10:

a: \(\Leftrightarrow-x^3+8x^3-12x^2+6x-1+1-3x+3x^2-x^3=0\)

\(\Leftrightarrow6x^3-9x^2+3x=0\)

\(\Leftrightarrow3x\left(2x^2-3x+1\right)=0\)

\(\Leftrightarrow x\left(2x-1\right)\left(x-1\right)=0\)

hay \(x\in\left\{0;\dfrac{1}{2};1\right\}\)

b: Đặt 3x-1=a; x-3=b

Theo đề, ta có: \(a^3+b^3-\left(a+b\right)^3=0\)

\(\Leftrightarrow a^3+b^3-a^3-b^3-3a^2b-3ab^2=0\)

\(\Leftrightarrow3ab\left(a+b\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-1=0\\x-3=0\\4-4x=0\end{matrix}\right.\Leftrightarrow x\in\left\{\dfrac{1}{3};3;1\right\}\)