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...
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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