One rule, three different functions.

Jozef Dobos shared this question 6 days ago
Answered

I'm trying to solve the equation


sqrt(x-2sqrt(x-1))=sqrt(x-1)-1.


To my surprise, Simplify(sqrt(x-2sqrt(x-1))) gives an unexpected result: sqrt(abs(x-1))-1.

Comments (4)

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Simplify will choose one of the branches in this case. For more control you can try:

Assume(x<2,Simplify(sqrt(x-2sqrt(x-1))))
Assume(x>2,Simplify(sqrt(x-2sqrt(x-1))))


https://wiki.geogebra.org/e...

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https://wiki.geogebra.org/e...


"Assume(x>2,Simplify(sqrt(x-2sqrt(x-1)))) yields sqrt(abs(x - 1)) + 1"


No, this yields sqrt(x - 1) + 1.


How do I know I have to distinguish these two cases when solving my equation?

Compare with


https://www.wolframalpha.co...

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I think the correct answer must be abs(sqrt(x - 1) - 1)

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I'm trying to solve my equation. See attached file.

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