How do I get the second value of x in this problem
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How do I get the second value of x in this problem

[From: ] [author: ] [Date: 11-09-20] [Hit: ]
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(x-18)^(2/5)=9

I got 261, but its telling me that there is another answer. How do I get it?

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(x - 18)^(2/5) = 9

x - 18 = 9^(5/2)

x - 18 = sqrt(9^5)

x - 18 = ± 243

x = 18 ± 243

x = 261 or - 225

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(x-18)^(2/5) = 9
[(x-18)^(2/5)]^5 = 9^5 = 59049
(x-18)² = 59049
(x-18) = ±√59049 = ±243
x = 18±243 = -225, 261

The two values of x which satisfy the equation are x = -225 and x = 261

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(x-18)^2/5 = 9 ----- raise both sides to the 5th power
==> (x-18)^2 = 9^5
==> x-18 = +/-sqrt( 9^5)
==> x = 18 +/- sqrt(3^10)
==> x = 18 +/- 3^5
==> x = 18 +/- 243
==> x = 261 or x = -255

-
u = (x - 18)^1/

u^2 = 9
u^2 - 9 = 0
(u - 3)(u + 3) = 0

u = 3 or u = - 3

replace u with (x - 18)^1/5

(x - 18)^1/5 = 3
x - 18 = 243
x = 261

or

(x - 18)^1/5 = - 3
x - 18 = - 243
x = - 225
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