How do you solve #\sqrt { y + 14} - \sqrt { y - 2} = 2#?

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Answer 1 · 2016-10-29T15:22:01

#sqrt(y + 14) = 2 + sqrt(y - 2)#

#(sqrt(y + 14))^2 = (2 + sqrt(y - 2))^2#

#y + 14 = 4 + 4sqrt(y - 2) + y - 2#

#12 = 4sqrt(y - 2)#

#3 = sqrt(y - 2)#

#3^2 = (sqrt(y - 2))^2#

#9 = y - 2#

#y = 11#

Check in the original equation.

#sqrt(11 + 14) - sqrt(11 - 2) =^? 2#

#5 - 3 = 2" "√#

Hopefully the helps!