3: ĐKXĐ: \(x\ge-\frac13\)
Ta có: \(\sqrt{3x+1}+\sqrt{x+3}+x-5=0\)
=>\(\sqrt{3x+1}-2+\sqrt{x+3}-2+x-1=0\)
=>\(\frac{3x+1-4}{\sqrt{3x+1}+2}+\frac{x+3-4}{\sqrt{x+3}+2}+\left(x-1\right)=0\)
=>\(\left(x-1\right)\left(\frac{3}{\sqrt{3x+1}+2}+\frac{1}{\sqrt{x+3}+2}+1\right)=0\)
=>x-1=0
=>x=1(nhận)
4: ĐKXĐ: x>=-3
Ta có: \(\sqrt{x+3}+\sqrt[3]{5x+3}=4\)
=>\(\sqrt{x+3}-2+\sqrt[3]{5x+3}-2=4-2-2=0\)
=>\(\frac{x+3-4}{\sqrt{x+3}+2}+\frac{5x+3-8}{\sqrt[3]{\left(5x+3\right)^2}+2\cdot\sqrt[3]{5x+3}+4}=0\)
=>\(\frac{x-1}{\sqrt{x+3}+2}+\frac{5x-5}{\sqrt[3]{\left(5x+3\right)^2}+2\cdot\sqrt[3]{5x+3}+4}=0\)
=>\(\left(x-1\right)\cdot\left(\frac{1}{\sqrt{x+3}+2}+\frac{5}{\sqrt[3]{\left(5x+3\right)^2}+2\cdot\sqrt[3]{5x+3}+4}=0\right)\)
=>x-1=0
=>x=1(nhận)
