Ta có:
\(f\left(x\right).g\left(x\right)+x^2\left[1-3.g\left(x\right)\right]=\dfrac{5}{2}\)
\(\Rightarrow f\left(x\right).g\left(x\right)+x^2-3.g\left(x\right).x^2-\dfrac{5}{2}=0\)
\(\Rightarrow g\left(x\right)\left[f\left(x\right)-3x^2\right]+x^2-\dfrac{5}{2}=0\)
Thay g(x) = x - 1 và f(x) = 3x2 - x + 1 vào ta được
\(\Rightarrow\left(x-1\right)\left(3x^2-x+1-3x^2\right)+x^2-\dfrac{5}{2}=0\)
\(\Rightarrow\left(x-1\right)\left(1-x\right)+x^2-\dfrac{5}{2}=0\)
\(\Rightarrow x-1-x^2+x+x^2-\dfrac{5}{2}=0\)
\(\Rightarrow2x-1-x^2+x^2-\dfrac{5}{2}=0\)
\(\Rightarrow2x-\dfrac{7}{2}=0\)
\(\Rightarrow2x=\dfrac{7}{2}\)
\(\Rightarrow x=\dfrac{7}{4}\)
