Question 1131612


{{{sqrt(5x+1) +sqrt(x+1) =sqrt(10x+6 )}}}....square both sides


{{{(sqrt(5x+1) +sqrt(x+1) )^2=(sqrt(10x+6 ))^2}}}


{{{(sqrt(5x+1))^2 +2sqrt(5x+1) *sqrt(x+1)+( sqrt(x+1) )^2=10x+6 }}}


{{{5x+1+2sqrt(5x+1) *sqrt(x+1)+x+1=10x+6 }}}


{{{6x+2+2sqrt((5x+1) (x+1))=10x+6 }}}


{{{2sqrt((5x+1) (x+1))=10x-6x+6 -2}}}


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


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


{{{sqrt((5x+1) (x+1))=2x+2}}}....square both sides


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


{{{(5x+1) (x+1)=4x^2+8x+4}}}


{{{5x^2 + 6 x + 1=4x^2+8x+4}}}


{{{5x^2 + 6 x + 1-4x^2-8x-4=0}}}


{{{x^2 -2x-3=0}}}...factor


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


{{{(x^2 +x)-(3x+3)=0}}}


{{{x(x +1)-3(x+1)=0}}}


{{{(x-3)(x+1)=0}}}


solutions:

{{{x=3}}}

{{{x=-1}}}