a: \(\Leftrightarrow x^2-4x-6=15\)
=>x2-4x-21=0
=>(x-7)(x+3)=0
=>x=-3 hoặc x=7
b: \(\Leftrightarrow4\sqrt{x-1}+6\sqrt{x-1}-8\sqrt{x-1}=6\sqrt{5}\)
\(\Leftrightarrow2\sqrt{x-1}=6\sqrt{5}\)
=>căn x-1=3 căn 5
=>x-1=45
=>x=46
a, \(\sqrt{x^2-4x-6}=\sqrt{15}\)
\(\Leftrightarrow\left(\sqrt{x^2-4x-6}\right)^2=\left(\sqrt{15}\right)^2\)
\(\Leftrightarrow x^2-4x-6=15\)
\(\Leftrightarrow x^2-4x-21=0\)
\(\Leftrightarrow\left(x-7\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-3\end{matrix}\right.\)
b, \(\sqrt{16x-16}+\sqrt{36x-36}-\sqrt{64x-64}=\sqrt{180}\)
\(\Leftrightarrow\sqrt{16\left(x-1\right)}+\sqrt{36\left(x-1\right)}-\sqrt{64\left(x-1\right)}=\sqrt{180}\)
\(\Leftrightarrow4\sqrt{x-1}+6\sqrt{x-1}-8\sqrt{x-1}=\sqrt{180}\)
\(\Leftrightarrow2\sqrt{x-1}=\sqrt{180}\)
\(\Leftrightarrow\left(2\sqrt{x-1}\right)^2=\left(\sqrt{180}\right)^2\)
\(\Leftrightarrow4\left(x-1\right)=180\)
\(\Leftrightarrow x-1=45\Leftrightarrow x=46\)
a, √x2−4x−6=√15x2−4x−6=15
⇔(√x2−4x−6)2=(√15)2⇔(x2−4x−6)2=(15)2
⇔x2−4x−6=15⇔x2−4x−6=15
⇔x2−4x−21=0⇔x2−4x−21=0
⇔(x−7)(x+3)=0⇔(x−7)(x+3)=0
⇔[x−7=0x+3=0⇔[x=7x=−3⇔[x−7=0x+3=0⇔[x=7x=−3
b, √16x−16+√36x−36−√64x−64=√18016x−16+36x−36−64x−64=180
⇔√16(x−1)+√36(x−1)−√64(x−1)=√180⇔16(x−1)+36(x−1)−64(x−1)=180
⇔4√x−1+6√x−1−8√x−1=√180⇔4x−1+6x−1−8x−1=180
⇔2√x−1=√180⇔2x−1=180
⇔(2√x−1)2=(√180)2⇔(2x−1)2=(180)2
⇔4(x−1)=180⇔4(x−1)=180
⇔x−1=45⇔x=46
a: ⇔x2−4x−6=15⇔x2−4x−6=15
=>x2-4x-21=0
=>(x-7)(x+3)=0
=>x=-3 hoặc x=7
b: ⇔4√x−1+6√x−1−8√x−1=6√5⇔4x−1+6x−1−8x−1=65
⇔2√x−1=6√5⇔2x−1=65
=>căn x-1=3 căn 5
=>x-1=45
=>x=46
