Questions on Algebra: Square root, cubic root, N-th root answered by real tutors!

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Question 149973: square root of T+3 minus the square root of T-2 equals the square root of 7-T: square root of T+3 minus the square root of T-2 equals the square root of 7-T
Answer by Fombitz(1741) About Me  (Show Source):
You can put this solution on YOUR website!
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