Question #05a32

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Answer 1 · 2015-07-18T20:20:40

#x=6#

#sqrt(x+19)+sqrt(x-2) = 7#

#sqrt(x+19) = 7-sqrt(x-2)#

#(sqrt(x+19))^2 = (7-sqrt(x-2))^2#

#x+19 = 49-14sqrt(x-2)+x-2#

#14sqrt(x-2) = 30-2 = 28#

#sqrt(x-2)=2#

#x-2 = 4#

#x=6#

Check for extraneous:

#sqrt(6+19)+sqrt(6-2) = sqrt 25+sqrt4 = 5+2=7#