Algebra

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Please help me solve:

[SQRT(x)]=-2
1.
[SQRT(2x2 - 1)]=x

  • Algebra -

    [SQRT(x)]=-2
    has no solution since by definition √ gives only positive result.

    for verification graph f(x) = √x + 2
    it never touches or crosses the x-axis

    for the second, I assume you mean
    √(2x^2-1) = x
    square both sides
    2x^2-1 = x^2
    x^2 = 1
    x = ±1
    but since we squared, both answers must be verfied.
    if x=1
    LS = √(2-1) = 1
    RS = 1, so it works

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

    so x = 1

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