Question

\(x^2-12+\frac{36}{x^2}-4x+\frac{24}{x}=5\)

Answer 1

sử dụng BDT cosi là ra bn à

Answer 2

\(x^2-12+\frac{36}{x^2}-4x+\frac{24}{x}=5\)

\(\Leftrightarrow x^2+\frac{36}{x^2}-4x+\frac{24}{x}=5+12\)

\(\Leftrightarrow x^2+\frac{36}{x^2}-4x+\frac{24}{x}=17\)

\(\Leftrightarrow x^2.x^2+\frac{36}{x^2}.x^2-4x.x^2+\frac{24}{x}.x^2=17x^2\)

\(\Leftrightarrow x^4+36-4x^3+24x=17x^2\)

\(\Leftrightarrow x^4+36-4x^3+24x=17x^2-17x^2\)

\(\Leftrightarrow x^4+36-4x^3+24x=0\)

\(\Leftrightarrow\left(x+1\right)\left(x-2\right)\left(x+3\right)\left(x-4\right)=0\)

\(\Rightarrow x\in\left\{-1;2;-3;4\right\}\)