Question 1192221


{{{sqrt(3x + 4) - sqrt(x+5) = 1  }}}

{{{sqrt(x + 5) + 1 = sqrt(3 x + 4)}}}

{{{(sqrt(x + 5) + 1)^2 = (sqrt(3 x + 4))^2}}}

{{{x + 2sqrt(x + 5) + 6=3x + 4}}}

 {{{2sqrt(x + 5) =3x-x + 4-6}}}

{{{2sqrt(x + 5) =2x -2}}}

{{{sqrt(x + 5) =x -1}}}

{{{(sqrt(x + 5))^2 =(x -1)^2}}}

{{{x + 5 =x^2 -2x+1}}}

{{{x^2 -2x+1-x-5=0}}}

{{{x^2 -3x-4=0}}}

{{{x^2 -3x-4=0}}}

{{{(x - 4) (x + 1) = 0}}}


solutions:
{{{x=4}}}
{{{x=-1}}}

verify solutions:


{{{sqrt(3(4) + 4) - sqrt(4+5)=1}}} 
{{{sqrt(16) - sqrt(9)=1 }}}
{{{4 - 3=1}}} 
{{{1=1}}} ->true


{{{sqrt(3(-1) + 4) - sqrt(-1+5)=1 }}}
{{{sqrt(1) - sqrt(4)=1 }}}
{{{1 - 2=1 }}}
{{{-1=1 }}}-> not true=> so, x=-1 is not a solution


the solution is: {{{x=4}}}