Solve the radical equation and check all proposed solutions. x-\sqrt{3x-2}

glasskerfu 2021-09-12 Answered
Solve the radical equation and check all proposed solutions.
\(\displaystyle{x}-\sqrt{{{3}{x}-{2}}}={4}\)

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Expert Answer

SoosteethicU
Answered 2021-09-13 Author has 8780 answers
Given equation is
\(\displaystyle{x}-\sqrt{{{3}{x}-{2}}}={4}\)
Rearranging the terms
\(\displaystyle{x}-{4}=\sqrt{{{3}{x}-{2}}}\)
Squaring both side
\(\displaystyle{\left({x}-{4}\right)}^{{2}}={\left(\sqrt{{{3}{x}-{2}}}\right)}^{{2}}\)
\(\displaystyle\Rightarrow{x}^{{2}}-{2}\times{4}\times{x}+{4}^{{2}}={3}{x}-{2}\)
\(\displaystyle\Rightarrow{x}^{{2}}-{8}{x}+{16}={3}{x}-{2}\)
\(\displaystyle\Rightarrow{x}^{{2}}-{11}{x}+{18}={0}\)
Now solve the quadratic equation
\(\displaystyle{x}^{{2}}-{11}{x}+{18}={0}\)
\(\displaystyle{x}^{{2}}-{9}{x}-{2}{x}+{18}={0}\)
\(\displaystyle{x}{\left({x}-{9}\right)}-{2}{\left({x}-{9}\right)}={0}\)
\(\displaystyle{\left({x}-{2}\right)}{\left({x}-{9}\right)}={0}\)
Hence, x=2,9
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