Solve for x sqrt(2x+5) = sqrt(x+2) + sqrt(2x-3).

Expert Answers

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

Let us square both sides:

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

==> (2x+5) = x+2 + 2x -3 + 2sqrt(2x^2 +x -6)

==> (2x+5) = 3x -1 + 2sqrt(2x^2 + x -6)

==> -x +6 = 2sqrt(x+2)(2x-3)

Square both sides again:

==> x^2 -12x + 36 = 4*(2x^2 + x - 6)

==> x^2 -12x +36 = 8x^2 +4x - 24

Group similar terms:

==> 7x^2 +16x -60 = 0

==> x1= [-16 + sqrt(25d + 4*7*60)]/14= (-16 + 44)14

             = 28/14= 2

==> x2= (-16 -44)/14= -60/14= -30/7

==> the solutions are:

x1= 2     and x2= -30/7

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