Question 342226
{{{sqrt(4y+5)-sqrt(y-1)=3}}}

{{{sqrt(4y+5)=sqrt(y-1)+3}}}
Square both sides,
{{{4y+5=(y-1)+6sqrt(y-1)+9}}}
{{{4y+5=y+8+6sqrt(y-1)}}}
{{{3y-3=6sqrt(y-1)}}}
{{{3(y-1)=6sqrt(y-1)}}}
{{{(y-1)=2sqrt(y-1)}}}
Use a substitution, let {{{u=y-1}}}
{{{u=2*sqrt(u)}}}
Square both sides,
{{{u^2=4u}}}
{{{u^2-4u=0}}}
{{{u(u-4)=0}}}
Two solutions:
{{{u=0}}}
{{{y-1=0}}}
{{{highlight(y=1)}}}
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{{{u-4=0}}}
{{{y-1-4=0}}}
{{{y-5=0}}}
{{{highlight(y=5)}}}