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

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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 Template:Tt 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 $\sqrt{2}$ 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 Template:Sqrt.  --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)