Question 661045

{{{sqrt(x-3)+1=sqrt(x+2)}}} ...raise both sides to power of {{{2}}}


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


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

{{{x-3+2sqrt(x-3)+1=x+2}}}

{{{2sqrt(x-3)=x-x+3-1+2}}}

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

{{{2sqrt(x-3)=4}}}...raise both sides to power of {{{2}}}

{{{(2sqrt(x-3))^2=4^4}}}

{{{4(x-3)=16}}} .. both sides divide by {{{4}}}

{{{4/4(x-3)=16/4}}} 

{{{x-3=4}}}

{{{x=4+3}}}


{{{highlight(x=7)}}}


check:

{{{sqrt(x-3)+1=sqrt(x+2)}}} 


{{{sqrt(7-3)+1=sqrt(7+2)}}} 


{{{sqrt(4)+1=sqrt(9)}}} 


{{{2+1=3}}} 

{{{3=3}}}