Wikipedia:Reference desk/Archives/Mathematics/2024 May 6

= May 6 =

Find
Given x=3+2√2, find √x - 1/√x 171.79.74.205 (talk) 17:01, 6 May 2024 (UTC)


 * the contradictory part is that in the end, you get (√x-1/√x)^2 = 4, which will give you ±2; but √x which is √3+2√2 can be written as √(2-√1)^2 which is 2-√1 hence √x - 1/√x = -2 171.79.74.205 (talk) 17:10, 6 May 2024 (UTC)
 * "... can be written ... ". No, it can't. Not sure if this is an honest question or just trolling. --RDBury (talk) 18:43, 6 May 2024 (UTC)
 * I'm not sure what they that is about but can I suggest that 1/(a+√b) = (a-√b)/{(a+√b)(a-√b)} might help? NadVolum (talk) 20:33, 6 May 2024 (UTC)
 * Clarify, please. Do you mean:
 * √x - (1/√x)
 * (√x - 1)/√x
 * √(x - 1)/√x
 * something else...?
 * I'd suggest using LaTeX/MathJax code within tags to format the expressions like $$\frac{\sqrt x-1}{\sqrt x}$$ etc. Please see WP:MATH for more info. --CiaPan (talk) 10:12, 7 May 2024 (UTC)
 * Sorry I misread the question and answered the wrong thing. But the square root of 3+2√2 is plus or minus 1+√2 and the original answer of ±2 is correct. NadVolum (talk) 11:07, 7 May 2024 (UTC)
 * √x is usually taken to mean the positive square root when x is positive. At least that's the notation used in Square root. That would make the answer 2. --RDBury (talk) 16:58, 7 May 2024 (UTC)
 * Only if you say the square root, and nobody has said that. It also doesn't matter whether the original √2 is positive or negative. NadVolum (talk) 17:07, 7 May 2024 (UTC)
 * The issue here is not a lack of the definite article, but the meaning of the symbol $$\sqrt{^~}.$$ Conventionally, when $$a$$ is a real number, $$\sqrt{a^2}$$ denotes the same as $$|a|,$$ so $$\sqrt2$$ is definitely positive. --Lambiam 18:15, 7 May 2024 (UTC)
 * The answer is 2 if the meaning of "√x−1/√x" is (√x) − (1/√x). But note that the question uses "√3+2√2" with the meaning √3 + 2√2. --Lambiam 18:25, 7 May 2024 (UTC)
 * Is this a homework problem? GalacticShoe (talk) 16:05, 7 May 2024 (UTC)
 * Possibly but they tried to check their solution. NadVolum (talk) 16:58, 7 May 2024 (UTC)