Question

\(\sqrt{4x-12}\)-\(\sqrt{9x-27}\)+\(\sqrt{\dfrac{25x-75}{\text{4}}}\)-3=0

Answer 1

\(\sqrt{4x-12}-\sqrt{9x-27}+\sqrt{\dfrac{25x-75}{4}}-3=0\left(dkxd:x\ge3\right)\)

\(\Leftrightarrow\sqrt{4\left(x-3\right)}-\sqrt{9\left(x-3\right)}+\sqrt{\dfrac{25}{4}\cdot\left(x-3\right)}=3\)

\(\Leftrightarrow2\sqrt{x-3}-3\sqrt{x-3}+\dfrac{5}{2}\sqrt{x-3}=3\)

\(\Leftrightarrow\dfrac{3}{2}\sqrt{x-3}=3\)

\(\Leftrightarrow\sqrt{x-3}=2\)

\(\Leftrightarrow x-3=4\)

\(\Leftrightarrow x=7\left(tmdk\right)\)

Vậy $x=7$.

$Toru$