Question

Giải phương trình :

1) 3\(\sqrt{ }\)2x-3 + 2\(\sqrt{ }\)8x-12 = \(\sqrt{ }\)18x-27 +9

Answer 1

Điều kiện: \(2x-3\ge0\Leftrightarrow x\ge\dfrac{3}{2}\)

\(3\sqrt{2x-3}+2\sqrt{8x-12}=\sqrt{18x-27}+9\)

\(3\sqrt{2x-3}+2\sqrt{4\left(2x-3\right)}-\sqrt{9\left(2x-3\right)}=9\)

\(3\sqrt{2x-3}+4\sqrt{2x-3}-3\sqrt{2x-3}=9\)

\(4\sqrt{2x-3}=9\)

\(x\ge\dfrac{3}{2}\)\(\Rightarrow16\left(2x-3\right)=81\)

\(2x-3=\dfrac{81}{16}\Leftrightarrow x=\dfrac{\dfrac{81}{16}+3}{2}=\dfrac{129}{32}\)