a)\(\sqrt{x^2+48}=4x-3+\sqrt{x^2+35}\)
\(\Leftrightarrow\sqrt{x^2+48}-7=4x-4+\sqrt{x^2+35}-6\)
\(\Leftrightarrow\dfrac{x^2+48-49}{\sqrt{x^2+48}+7}=4\left(x-1\right)+\dfrac{x^2+35-36}{\sqrt{x^2+35}+6}\)
\(\Leftrightarrow\dfrac{x^2-1}{\sqrt{x^2+48}+7}-4\left(x-1\right)-\dfrac{x^2-1}{\sqrt{x^2+35}+6}=0\)
\(\Leftrightarrow\left(x-1\right)\left(\dfrac{x+1}{\sqrt{x^2+48}+7}-4-\dfrac{x+1}{\sqrt{x^2+35}+6}\right)=0\)
\(\Rightarrow x-1=0\Rightarrow x=1\)
b)\(\left(\sqrt{x-1}+1\right)^3+2\sqrt{x-1}=2-x\)
\(pt\Leftrightarrow\left(\sqrt{x-1}+1\right)^3-1+2\sqrt{x-1}=1-x\)
\(\Leftrightarrow\left(\sqrt{x-1}+1-1\right)\left(\left(\sqrt{x-1}+1\right)^6+\left(\sqrt{x-1}+1\right)^3+1\right)+2\sqrt{x-1}-\left(1-x\right)=0\)
\(\Leftrightarrow\sqrt{x-1}\left(\left(\sqrt{x-1}+1\right)^6+\left(\sqrt{x-1}+1\right)^3+1\right)+2\sqrt{x-1}+x-1=0\)
\(\Leftrightarrow\sqrt{x-1}\left(\left(\sqrt{x-1}+1\right)^6+\left(\sqrt{x-1}+1\right)^3+3+\sqrt{x-1}\right)=0\)
Dễ thấy: \(\left(\sqrt{x-1}+1\right)^6+\left(\sqrt{x-1}+1\right)^3+3+\sqrt{x-1}>0\)
\(\Rightarrow\sqrt{x-1}=0\Rightarrow x-1=0\Rightarrow x=1\)
