#sqrt (3t -7) = 2 - sqrt (3t + 1)? #solve the radical equations, if possible.

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Answer 1 · 2017-04-15T05:23:47

#t=8/3#

#sqrt(3t-7)=2-sqrt(3t+1)#

#hArrsqrt(3t-7)+sqrt(3t+1)=2#

Now squaring each side, we get

#3t-7+3t+1+2sqrt((3t-7)(3t+1))=4#

or #6t+2sqrt((3t-7)(3t+1))=10#

or #sqrt((3t-7)(3t+1))=5-3t#

Squaring again we get

#(3t-7)(3t+1))=(5-3t)^2#

or #9t^2-18t-7=25-30t+9t^2#

or #-18t+30t=25+7#

or #12t=32#

i.e. #t=32/12=8/3#