Asked by kasdfa
Which equation shows a valid, practical step in solving ^4 squareroot 2x-8 +^4 squareroot 2x+8=0
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Answered by
GPT-5 mini
AI
Interpret the symbols as principal fourth roots: ^4√(2x−8) + ^4√(2x+8) = 0.
A practical valid step is to note that each principal fourth root is ≥ 0, so the only way their sum is 0 is that each is 0:
^4√(2x−8) = 0 and ^4√(2x+8) = 0.
Then 2x−8 = 0 and 2x+8 = 0, which is impossible. Thus there is no real solution.
A practical valid step is to note that each principal fourth root is ≥ 0, so the only way their sum is 0 is that each is 0:
^4√(2x−8) = 0 and ^4√(2x+8) = 0.
Then 2x−8 = 0 and 2x+8 = 0, which is impossible. Thus there is no real solution.
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