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Help me understand the meaning of "solve/ find the solution/ what are the roots" using the following?

x-7=sqrt(x-5)

Update:

I think "it is necessary to check the converse proposition by substitution in the original equation"

Update 2:

Please ref to, e.g., for proper answer: Richardson, M. (1982 ). College Algebra. 3rd Ed., Prentice-Hall, Eaglewood Cliffs

Update 3:

It is necessary to check the converse proposition by substitution in the original equation(s)

Checking is not merely a superfluous step but an essential part of the work

Please ref to, e.g.,

Richardson, M. (1982 ). College Algebra. 3rd Ed., Prentice-Hall, Eaglewood Cliffs

Solving involves three steps

(1) Find the candidate values;

(2) Determine which values satisfy the original equation(s); and

(3) State the selected values.

3 Answers

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  • ssssh
    Lv 5
    1 decade ago
    Favorite Answer

    (x-7) = √ (x-5)

    keep in mind that x must be >or= 7 because you are solving for the primary sq.root which must be 0 or positive

    square both sides and get

    x^2 - 14x + 49 = x - 5

    this becomes

    x^2 - 15x + 54 = 0

    factor and solve

    (x - 9)(x - 6) = 0

    so x = 9 or x = 6

    the only acceptable answer is x = 9 [see above]

    ~~

    If you substitute these values into the original eqn.

    you get

    9-7 = sqrt[9-4] so 2 = sqrt[4] is correct and 9 is a solution

    6-7 = sqrt[6-5] gives -1 = sqrt[1] which is not correct because sqrt[1] means the primary or positive sqrt which is positive 1 not -1 ............. so 6 is not an acceptable solution

    ~~

  • ?
    Lv 4
    5 years ago

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  • Anonymous
    1 decade ago

    To solve means to find the unknown value in the given problem.

    To find the solution also means the same.

    I guess......

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