Question 149973
{{{sqrt(T+3)-sqrt(T-2)=sqrt(7-T)}}}
First, square both sides.
{{{(sqrt(T+3))^2-2sqrt(T+3)sqrt(T-2)+(sqrt(T+2))^2=(sqrt(7-T))^2}}}
{{{(T+3)-2sqrt((T+3)(T-2))+(T-2)=7-T}}}
{{{(2T+1)-2sqrt((T+3)(T-2))=-T+7}}}
{{{-2sqrt((T+3)(T-2))=-3T+6}}}
Square both sides.
{{{4(T+3)(T-2)=9T^2-36T+36}}}
{{{4(T^2+T-6)=9T^2-36T+36}}}
{{{4T^2+4T-24=9T^2-36T+36}}}
{{{5T^2-40T+60=0}}}
{{{T^2-8T+12=0}}}
{{{(T-2)(T-6)=0}}}
First solution
{{{T-2=0}}}
{{{T=2}}}
Second solution
{{{T-6=0}}}
{{{T=6}}}