a, \(2\sqrt{2x^2+3}-10=0\)
\(\Leftrightarrow\sqrt{2x^2+3}=5\)
\(\Leftrightarrow2x^2+3=25\)
\(\Leftrightarrow x^2=11\)
\(\Leftrightarrow x=\pm\sqrt{11}\)
b, \(\sqrt{x^2+6}+3=2x\)
\(\Leftrightarrow\sqrt{x^2+6}=2x-3\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2+6=\left(2x-3\right)^2\\2x-3>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2+6=4x^2+9-12x\\x>\dfrac{3}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x^2-12x+3=0\\x>\dfrac{3}{2}\end{matrix}\right.\)
\(\Leftrightarrow x=2+\sqrt{3}\)
c, ĐK: \(x\ge\dfrac{3}{5}\)
\(pt\Leftrightarrow3\sqrt{4\left(5x-3\right)}-\dfrac{2}{3}\sqrt{9\left(5x-3\right)}=8\)
\(\Leftrightarrow6\sqrt{5x-3}-2\sqrt{5x-3}=8\)
\(\Leftrightarrow4\sqrt{5x-3}=8\)
\(\Leftrightarrow\sqrt{5x-3}=2\)
\(\Leftrightarrow5x-3=4\)
\(\Leftrightarrow x=\dfrac{7}{5}\left(tm\right)\)
d: Ta có: \(\sqrt{4x-12}-3\sqrt{x-3}=10-\sqrt{9x-27}\)
\(\Leftrightarrow2\sqrt{x-3}=10\)
\(\Leftrightarrow x-3=25\)
hay x=28
e: Ta có: \(2\sqrt{9x+45}+\sqrt{4x+20}=24-\sqrt{16x+80}\)
\(\Leftrightarrow6\sqrt{x+5}+2\sqrt{x+5}=24-4\sqrt{x+5}\)
\(\Leftrightarrow4\sqrt{x+5}=24\)
\(\Leftrightarrow x+5=36\)
hay x=31
d, ĐK: \(x\ge3\)
\(\sqrt{4x-12}-3\sqrt{x-3}=10-\sqrt{9x-27}\)
\(\Leftrightarrow2\sqrt{x-3}-3\sqrt{x-3}=10-3\sqrt{x-3}\)
\(\Leftrightarrow2\sqrt{x-3}=10\)
\(\Leftrightarrow x-3=25\)
\(\Leftrightarrow x=28\left(tm\right)\)
a: Ta có: \(2\sqrt{2x^2+3}-10=0\)
\(\Leftrightarrow\sqrt{2x^2+3}=5\)
\(\Leftrightarrow2x^2+3=25\)
\(\Leftrightarrow2x^2=22\)
\(\Leftrightarrow x^2=11\)
hay \(x\in\left\{\sqrt{11};-\sqrt{11}\right\}\)
b: Ta có: \(\sqrt{x^2+9}+3=2x\)
\(\Leftrightarrow\sqrt{x^2+9}=2x-3\)
\(\Leftrightarrow x^2+9=4x^2-12x+9\)
\(\Leftrightarrow3x^2-12x=0\)
\(\Leftrightarrow3x\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=4\left(nhận\right)\end{matrix}\right.\)
c: Ta có: \(3\sqrt{20x-12}-\dfrac{2}{3}\sqrt{45x-27}=8\)
\(\Leftrightarrow6\sqrt{5x-3}-2\sqrt{5x-3}=8\)
\(\Leftrightarrow4\sqrt{5x-3}=8\)
\(\Leftrightarrow5x-3=4\)
\(\Leftrightarrow5x=7\)
hay \(x=\dfrac{7}{5}\)
e, ĐK: \(x\ge-5\)
\(2\sqrt{9x+45}+\sqrt{4x+20}=24-\sqrt{16x+80}\)
\(\Leftrightarrow6\sqrt{x+5}+2\sqrt{x+5}=24-4\sqrt{x+5}\)
\(\Leftrightarrow12\sqrt{x+5}=24\)
\(\Leftrightarrow x+5=4\)
\(\Leftrightarrow x=-1\left(tm\right)\)
