Question

PLEASE HELP, BRAINLIEST FOR CORRECT ANSWERS!!!

Answer 1

9514 1404 393

Answer:

1. {-234, 252}
2. {81}
3. {-16, 2}

Step-by-step explanation:

1. (x -9)^(2/5) = 9

  (x -9) = ±√(9^5) = ±3^5 = ±243 . . . . raise both sides to the 5/2 power

  x = 9 ±243 . . . . . add 9

  x = {-234, 252}

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2. √x -√(x-32) = 2

  x -2√(x(x-32)) +(x-32) = 4 . . . . . square both sides

  -2√(x(x -32)) = 36 -2x . . . . . . . . add 32-2x

  √(x(x -32)) = x -18 . . . . . . . . . . . divide by -2

  x(x -32) = (x -18)^2 . . . . . . . . . . .square both sides

  x^2 -32x = x^2 -36x +324 . . . . eliminate parentheses

  4x = 324 . . . . . . . . . add 36x-x^2 to both sides

  x = {81} . . . . . . . . . . . . divide by 4

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3. (x^2 +14x)^(1/5) = 2

  x^2 +14x = 32 . . . . . . . . raise both sides to the 5th power

  x^2 +14x -32 = 0 . . . . . .subtract 32

  (x +16)(x -2) = 0 . . . . . . . factor

  x = {-16, 2} . . . . . . . . . . . values of x that make the factors zero

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Additional comment

Sometimes equations of this type have extraneous solutions. In order to avoid finding those, we have written each original equation in the form f(x) = 0 for graphing purposes. Then the x-intercepts are the solutions.