Question

Help please!
what is the soultion
radical 5x+1 - radical x=5
x = 0
x = 16 and x = 0
x = 16
x = 16 and x = 1

Answer 1

\[\large \sqrt{5x+1}-\sqrt{x}=5\]


\[\large \sqrt{5x+1}=5+\sqrt{x}\]


\[\large \left(\sqrt{5x+1}\right)^2=\left(5+\sqrt{x}\right)^2\]


\[\large 5x+1=\left(5+\sqrt{x}\right)^2\]


\[\large 5x+1=\left(5+\sqrt{x}\right)\left(5+\sqrt{x}\right)\]


\[\large 5x+1=5\left(5+\sqrt{x}\right)+\sqrt{x}\left(5+\sqrt{x}\right)\]


\[\large 5x+1=25+5\sqrt{x}+\sqrt{x}*5+\sqrt{x}*\sqrt{x}\]


\[\large 5x+1=25+5\sqrt{x}+5\sqrt{x}+\left(\sqrt{x}\right)^2\]


\[\large 5x+1=25+10\sqrt{x}+x\]


\[\large 5x+1-x-25=10\sqrt{x}\]


\[\large 4x-24=10\sqrt{x}\]


\[\large \left(4x-24\right)^2=\left(10\sqrt{x}\right)^2\]


\[\large 16x^2-192x+576=100x\]


\[\large 16x^2-192x+576-100x=0\]


\[\large 16x^2-292x+576=0\]


I'll let you finish. Make sure to check any/all solutions you get.

Answer 2

Thanks jim!!

Answer 3

sure thing