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Algebra II

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A student is asked to solve b2 + a2 = c2 for a and gives the following solution. Assume all variables represent positive Real Numbers.

b2 + a2 = c2
pb2 + a2 = pc2
b + a = c
a = c-b

Explain the mistake(s) made by the student and provide the correct solution.

  • Algebra II -

    p? do you mean √?
    √(b^2+a^2) = √c^2
    clearly the next step is flawed.

    √(b^2+a^2) ≠ b+a

    while √(b^2*a^2) = √b^2 * √a^2,
    √(b^2+a^2) ≠ √b^2 + √a^2

    I figure you can take it from there

  • Algebra II -

    a^2+b^2=c^2

    a^2=c^2-b^2

    a=square root of (c^2-b^2)

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