Question

Tìm x

\(2x+2\sqrt{x}-18\) = 0

Answer 1

ĐKXĐ : \(x\ge0\)

\(2x+2\sqrt{x}-18=0\)

\(\Leftrightarrow x+\sqrt{x}-9=0\)

\(\Leftrightarrow x+2\sqrt{x}\frac{1}{2}+\frac{1}{4}-\frac{37}{4}=0\)

\(\Leftrightarrow\left(\sqrt{x}+\frac{1}{2}\right)^2=\frac{37}{4}\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}+\frac{1}{2}=\frac{\sqrt{37}}{2}\\\sqrt{x}+\frac{1}{2}=\frac{-\sqrt{37}}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=\frac{-1+\sqrt{37}}{2}\\\sqrt{x}=\frac{-1-\sqrt{37}}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{38-2\sqrt{37}}{4}\left(TM\right)\\\text{vô nghiệm}\end{matrix}\right.\)

Answer 2

ĐK: \(x\ge0\)

\(2x+2\sqrt{x}-18=0\Leftrightarrow2\left(\sqrt{x}-\frac{-1+\sqrt{37}}{2}\right)\left(\sqrt{x}-\frac{-1-\sqrt{37}}{2}\right)=0\)

Suy ra \(\left[{}\begin{matrix}\sqrt{x}=\frac{-1+\sqrt{37}}{2}\\\sqrt{x}=\frac{-1-\sqrt{37}}{2}\left(L\right)\end{matrix}\right.\). Đến đây chắc ok rồi ạ.

Answer 3

ĐK: \(x\ge0\)

PT \(\Leftrightarrow2\left(\sqrt{x}-\frac{-1+\sqrt{37}}{2}\right)\left(\sqrt{x}-\frac{-1-\sqrt{37}}{2}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=\frac{-1+\sqrt{37}}{2}\\\sqrt{x}=\frac{-1-\sqrt{37}}{2}\left(L\right)\end{matrix}\right.\)

Đến đây chắc ok rồi ạ!