Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 years ago

Solve √(2x+5)-√(x-1)=2?

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  • Harish
    Lv 7
    7 years ago
    Favorite Answer

    √(2x + 5) - √(x - 1) = 2

    3x + 4 - 2√(2x + 5)√(x - 1) = 4

    9x^2 = 8x^2 + 12x - 20

    x^2 - 12x + 20 = 0

    (x - 10)(x - 2) = 0

    Solutions:

    x = 2

    x = 10

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  • Niall
    Lv 7
    7 years ago

    Isolate one of the square roots:

    √(2x + 5) = 2 + √(x - 1)

    Square both sides to cancel out the square root:

    2x + 5 = 4 + 4√(x - 1) + x - 1

    Isolate the square root term again:

    x + 2 = 4√(x - 1)

    Square both sides to cancel out the square root:

    x^2 + 4x + 4 = 16(x - 1)

    Expand the brackets:

    x^2 + 4x + 4 = 16x - 16

    Move everything to one side:

    x^2 - 12x + 20 = 0

    Factor it out:

    (x - 10)(x - 2) = 0

    x = 2, 10

    Whenever you square both sides always check your solutions because sometimes a false/extraneous solution is created. In this case both solutions fit.

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  • Anonymous
    7 years ago

    √(2x+5)-√(x-1)=2

    (2x+5)-(x-1)=4

    x+4= 4

    x=0

    Source(s): batman
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