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sqrt(x+5) + sqrt(x-3) = 4

First let us square both sides:

[sqrt(x+5) + sqrt(x-3)]^2 = 16

==> (x+5) + 2sqrt(x+5)(x-3) + (x-3) = 16

Group similar terms:

==> 2x + 2 + 2sqrt(x^2 + 2x - 15) = 16

divide by 2:

==> x + 1 + sqrt(x^2 + 2x - 15) = 8

Move x + 1 to the right sides:

==> sqrt(x^2 + 2x - 15) = 7x

Now square both sides again:

==> x^2 + 2x - 15 = (7-x)^2

==> x^2 + 2x - 15 = 49-14x + x^2

==> 16x = 64

==> x= 64/16 = 4

==> x= 4

Approved by eNotes Editorial Team

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