9514 1404 393
Answer:
- {-234, 252}
- {81}
- {-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.
