Question

Tìm x:

\(\sqrt{4x-4}\)+\(\sqrt{25x-25}\)+\(\sqrt{81x-81}\)=\(-\)1

Giải chi tiết nha!

Answer 1

ĐK: \(x\ge1\)

Ta có:

\(\sqrt{4x-4}+\sqrt{25x-25}+\sqrt{81x-81}=1\)

\(\Rightarrow\sqrt{4\left(x-1\right)}+\sqrt{25\left(x-1\right)}+\sqrt{81\left(x-1\right)}=1\)

\(\Rightarrow2\sqrt{x-1}+5\sqrt{x-1}+9\sqrt{x-1}=1\)

\(\Rightarrow16\sqrt{x-1}=1\)

\(\Rightarrow\sqrt{x-1}=\dfrac{1}{16}\)

\(\Rightarrow\left[{}\begin{matrix}x-1=\dfrac{1}{4}\\x-1=-\dfrac{1}{4}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{4}\\x=\dfrac{3}{4}\end{matrix}\right.\)