Question 76685
I have been trying to figure this out. I couldn't do it the conventional way, but I did find the answer doing guess and check. Please help me find the right way to solve it.
{{{ sqrt( x+14 ) }}}-{{{ sqrt( x-10 ) }}}= 2
{{{sqrt(x+14)-sqrt(x-10)+sqrt(x-10)=2+sqrt(x-10)}}}
{{{sqrt(x+14)=2+sqrt(x-10)}}}
{{{(sqrt(x+14))^2=(2+sqrt(x-10))^2}}}
{{{x+14=(2+sqrt(x-10))(2+sqrt(x-10))}}}
{{{x+14=4+2sqrt(x-10)+2sqrt(x-10)+sqrt(x-10)^2}}}
{{{x+14=4+4sqrt(x-10)+x-10}}}
{{{x+14=4sqrt(x-10)+x-6}}}
{{{x-x+14+6=4sqrt(x-10)+x-x-6+6}}}
{{{20=4sqrt(x-10)}}}
{{{20/4=4sqrt(x-10)/4}}}
{{{5=sqrt(x-10)}}}
{{{(5)^2=sqrt(x-10)^2}}}
{{{25=x-10}}}
{{{25+10=x-10+10}}}
{{{35=x}}}
Check to make sure it's not extraneous:
{{{sqrt(35+14)-sqrt(35-10)=2}}}
{{{sqrt(49)-sqrt(25)=2}}}
{{{7-5=2}}}
{{{2=2}}} It's valid:
{{{highlight(x=35)}}}
Happy Calculating!!!!