How do you evaluate #\sqrt { 2x + 1} - \sqrt { x - 10} = 2\sqrt { 3}#?

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Answer 1 · 2017-04-13T13:20:12

#x=(13,37)#

For feasibility we need

#2x+1 ge 0# and #x ge 0# then #x ge 10#

now looking to the constant coefficient #2sqrt3# we can choose

#x = 13# and then

#sqrt(27)-sqrt(3)=3sqrt3-sqrt3=2sqrt3#

Another choice is with #x=37# so

#sqrt75-sqrt37=5sqrt3-3sqrt3=2sqrt3#

so the real solutions are

#x=(13,37)#