Wolfram|Alpha gives me no solution exists, but I could solve the problem: (x+2*(x-1)^0.5)^0.5-(x-2*(x-1)^0.5)^0.5=3
Plug that solution into the equation to see if it actually works.
Hi
Yes, my solution gave me a false response, but I can’t understand this discrepancy. Anyway, have a nice day.
There is a mistake in your first step. When you take the square of an equation, you cannot write the double implication <==> but only ==>.
Thanks to everyone for your responses.
Gianluca nailed it.
I spot careless uses of implications elsewhere in the sheet too. The silent use of the rule Sqrt[a] Sqrt[b] == Sqrt[a*b] is problematic. However, in this case the faulty solution x=13/4 is introduced not in the first step, but in the very last step: x=13/4 does not satisfy the condition pt. x<2.
Yep, you’re right. I’m so stupid and I feel miserable wasting everybody’s time because I wasn’t attentive.
Radicals are tricky. Equations with radicals, doubly so. I have learnt from your nice example. I hope you have too.