Question 884241
{{{sqrt(7x+1)-sqrt(5x+4)=1}}}
{{{(7x+1)-2sqrt((7x+1)(5x+4))+5x+4=1}}}
{{{12x+5-2sqrt((7x+1)(5x+4))=1}}}
{{{12x+4=2sqrt((7x+1)(5x+4))}}}
{{{4(3x+1)=2sqrt((7x+1)(5x+4))}}}
{{{2(3x+1)=sqrt((7x+1)(5x+4))}}}
{{{4(9x^2+6x+1)=35x^2+33x+4}}}
{{{36x^2+24x+4=35x^2+33x+4}}}
{{{x^2-9x=0}}}
{{{x(x-9)=0}}}
Two solutions:
{{{x=0}}}
and
{{{x-9=0}}}
{{{x=9}}}
Verifying the solutions:
{{{sqrt(7x+1)-sqrt(5x+4)=1}}}
{{{sqrt(7(0)+1)-sqrt(5(0)+4)=1}}}
{{{1-2=1}}}
False, not a real solution.
{{{sqrt(7x+1)-sqrt(5x+4)=1}}}
{{{sqrt(7(9)+1)-sqrt(5(9)+4)=1}}}
{{{sqrt(64)-sqrt(49)=1}}}
{{{8-7=1}}}
{{{1=1}}}
True.
{{{highlight_green(x=9)}}}