Question

Giải pt:b)\(8x^3-12x^2+6x-5=0\)

a)\(x^3-\sqrt{3}x^2-x+3\sqrt{3}=0\)

b

Answer 1

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

\(\Leftrightarrow\left(2x\right)^3-3.\left(2x\right)^2.1+3.2x.1^2-1=4\)

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

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

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

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

Answer 2

$8x^3-12x^2+6x-5=0$

$\iff {\left(2x\right)}^3-3.{\left(2x\right)}^2.1+3.2x{.1}^2-1=4$

$\iff {\left(2x-1\right)}^3=4$

$\iff 2x-1=\sqrt[3]{34}$

$\iff 2x=\sqrt[3]{34}+1$

$\iff x=\frac{\sqrt[3]{34}+1}{2}$