Question #69e1d

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Answer 1 · 2016-10-19T07:21:25

#x = 80/9#

#sqrt(20-x) + 8 = sqrt(9-x) + 11#

#=> sqrt(20-x) = sqrt(9-x)+3#

#=> (sqrt(20-x))^2 = (sqrt(9-x)+3)^2#

#=> 20-x = (sqrt(9-x))^2+2(3)sqrt(9-x)+3^2#

#=> 20-x = 9-x+6sqrt(9-x)+9#

#=> 2 = 6sqrt(9-x)#

#=> sqrt(9-x) = 1/3#

#=> (sqrt(9-x))^2 = (1/3)^2#

#=> 9-x = 1/9#

#=> x = 9-1/9#

#=> x = 80/9#

Checking our result:

#sqrt(20-80/9)+8 = sqrt(100/9)+8#

#=10/3+8#

#=34/3#

#=1/3+11#

#=sqrt(1/9)+11#

#=sqrt(9-80/9) + 11#

as desired.