ALGEBRA

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When solving a rational equation, why is it necessary to perform a check?

  • ALGEBRA -

    When performing operations, like "squaring both sides", sometimes roots are introduced that were not part of the original relation.

    e.g.

    let x = 4, and only 4
    square both sides
    x^2 = 16
    now take √
    √(x^2) = √16
    ± x = 4
    x = ±4 , we now a "new" root

  • ALGEBRA -

    So inother words, we need to make that solutions are not those of original equations??

  • ALGEBRA -

    I will give you another example

    solve √(3x+10) = x+2
    square both sides
    3x+10 = x^2 + 4x + 4
    x^2 + x - 6 = 0
    (x+3)(x-2) = 0
    x = -3 or x = 2

    check: (in original)
    if x=2
    LS = √(6+10) = √16 = 4
    RS = 2+2 = 4 , checks

    if x = -3
    LS = √(-9+1) = 1
    RS = -3+2 = -1 , does not work

    so x = 2

  • ALGEBRA -

    I still do not understand it.

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