Question 342200
{{{sqrt(2x-1)-sqrt(x-5) = 3}}}
{{{sqrt(2x-1)=sqrt(x-5) + 3}}}
Square both sides,
{{{2x-1=(x-5)+6sqrt(x-5)+9}}}
{{{2x-1=(x+4)+6sqrt(x-5)}}}
{{{x-5=6sqrt(x-5)}}}
Use a substitution, let {{{u=x-5}}}
{{{u=6sqrt(u)}}}
Square both sides,
{{{u^2=36u}}}
{{{u^2-36u=0}}}
{{{u(u-36)=0}}}
Two solutions:
{{{u=0}}}
{{{x-5=0}}}
{{{highlight(x=5)}}}
.
.
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{{{u-36=0}}}
{{{u=36}}}
{{{x-5=36}}}
{{{highlight(x=41)}}}