Algebra

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The only solution to sqrt (2x+3) - sqrt(x+1) = 1 is x = 3
I think that is true but I'm not sure if I was suppose to separate this equation I just put the 3 in the place of the x and it was true but should I have done it differently?

  • Algebra -

    The answer is 3 and -1, from Wolframealpha

    I arrived at the - 1 answer, but not sure if the way I solved it is correct and just luck that I got the correct answer of -1!!

    maybe a tutor will step in an answer.

  • Algebra -

    x = 3 does not satisfy the equation as a solution.
    LS = (6+3) - √4
    = 9-2
    = 7
    RS = 1
    LS ≠ RS, so x ≠ 3

    let's solve it ...
    (2x+3) - sqrt(x+1) = 1
    2x + 3 - 1 = √(x+1)
    2x+2 = √(x+1)
    square both sides
    4x^2 + 8x + 4 = x+1
    4x^2 + 7x + 3 = 0
    (x+1)(4x+3) = 0
    x = -1 or x = -3/4

    if x = -1
    LS = (-2+3) - √0
    = 1-0 = 0
    = RS

    if x = -3/4
    LS = 2(-3/4) + 3 - √(1/4)
    = 3/2 - 1/2 = 1
    = RS

    so x = 0 or x = -3/4

  • ARGHH! Algebra -

    Forget about my solution above,
    Just plain ol' did not see that first square root sign!

  • 2nd try .... Algebra -

    √(2x+3) = √(x+1) + 1
    square both sides
    2x+3 = x+1 + 2√(x+1) + 1
    x + 1 = 2√(x+1)
    square again ...
    x^2 + 2x + 1 = 4(x+1)
    x^2 - 2x - 3 = 0
    (x+1)(x-3) = 0
    x = -1 or x = 3

    checking both,since we squared.

    if x = -1
    LS = √(-2+3) - √0
    = √1-√0 = 1 = RS

    if x = 3
    LS = √9 - √4
    = 3-2
    = 1 = RS

    So x = -1 or x = 3

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