Question

Giải pt bằng cách pt thành nhân tử

7. \(3x^3 + 3x^2 + 3x = -1\)

8. \(8x^3 - 12x^2 + 6x - 5 = 0\)

9. \(x^3 - x^2 - x = \frac{1}{3}\)

10. \(3(1 + x + x^2)^2 = (1 + x^2 + x^4)\)

Answer 1

\(7.3x^3+3x^2+3x=-1\)

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

\(\Leftrightarrow x^3+3x^2+3x+1=-2x^3\)

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

\(\Leftrightarrow x+1=-\sqrt[3]{2}x\)

\(\Leftrightarrow x=\dfrac{-1}{1+\sqrt[3]{2}}\)

\(8.8x^3-12x^2+6x-5=0\)

\(\Leftrightarrow8x^3-12x^2+6x-1-4=0\)

\(\Leftrightarrow\left(2x^3-1\right)^3=4\)

\(\Leftrightarrow2x-1=\sqrt[3]{4}\)

\(\Leftrightarrow x=\dfrac{\sqrt[3]{4}+1}{2}\)