SOLUTION: the square root of 2x plus three minus the square root ofx plus one equals one

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Question 85836: the square root of 2x plus three minus the square root ofx plus one equals one
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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the square root of 2x plus three minus the square root ofx plus one equals one
:
Here it is step-by-step, the idea is to perform algebra operations that will get rid of the radicals; Leaving us with a quadratic equation that we solve
:
sqrt%282x+%2B+3%29 - sqrt%28x%2B1%29 = 1
:
add sqrt%28x%2B1%29 to both sides
sqrt%282x+%2B+3%29 = sqrt%28x%2B1%29 + 1
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Square both sides:
2x + 3 = (x+1) + 2*sqrt(x+1) + 1; FOILed [(sqrt(x+1) + 1] * [sqrt(x+1) + 1]
:
2x + 3 = x + 2 + 2*sqrt(x+1)
:
2x - x + 3 - 2 = 2*sqrt(x+1)
:
x + 1 = 2*Sqrt(x+1)
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Square both sides again:
x^2 + 2x + 1 = 4(x+1); FOILed (x+1)*(x+1)
:
x^2 + 2x + 1 = 4x + 4
:
x^2 + 2x - 4x + 1 - 4 = 0
:
x^2 - 2x - 3 = 0
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Factors to:
(x - 3)(x + 1 ) = 0
:
x = +3
and
x = -1
:
Check both solutions by substitution in the original equation.