Question

[Haanh Phan]

Giải pt 

X√x +4√x +12=7x 

Answer 1

[FL.Han_]

đk: \(x\ge0\)

\(x\sqrt{x}+4\sqrt{x}+12=7x\)

\(\Leftrightarrow\left(x+4\right)\sqrt{x}=7x-12\)

\(\Leftrightarrow\left(x+4\right)^2\cdot x=\left(7x-12\right)^2\)

\(\Leftrightarrow x^3+8x^2+16x=49x^2-168x+144\)

\(\Leftrightarrow x^3-41x^2+184x-144=0\)

\(\Leftrightarrow\left(x^3-x^2\right)-\left(40x^2-40x\right)+\left(144x-144\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^2-40x+144\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-4\right)\left(x-36\right)=0\)

=> \(x\in\left\{1;4;36\right\}\)