Question

Giải phương trình : \(x^3-x^2-x=\frac{1}{3}\)

 

Answer 1

Ta có 

3(x³-x²-x)=1

(=) 3x³ - 3x² - 3x =1

(=) 4x³ - x³ -3x² -3x =1

(=) 4x³ = x³ +3x² +3x +1

(=) 4x³ = (x+1)³

=> x=\(\frac{x+1}{\sqrt[3]{4}}\)

=> x-\(\frac{x}{\sqrt[3]{4}}=\frac{1}{\sqrt[3]{4}}\)

=> x(1-\(\frac{1}{\sqrt[3]{4}}\)) =\(\frac{1}{\sqrt[3]{4}}\)

=> x \(\frac{\sqrt[3]{4}-1}{\sqrt[3]{4}}=\frac{1}{\sqrt[3]{4}}\)

=> x =\(\frac{1}{\sqrt[3]{4}-1}\)