If \(a=8-4\sqrt{2}\) then find the value of :
\[ \dfrac{a+2}{a-2} - \dfrac{a+2\sqrt{2}}{a-2\sqrt{2}}\]
Note by
Nihar Mahajan
3 years, 7 months ago
No vote yet
1 vote
Easy Math Editor
*italics*or_italics_**bold**or__bold__paragraph 1
paragraph 2
[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
Sort by:
Top Newest\(\begin{equation} \begin{split} \dfrac{a+2}{a-2} - \dfrac{a+2\sqrt{2}}{a-2\sqrt{2}} & = \dfrac{8-4\sqrt{2}+2}{8-4\sqrt{2}-2} - \dfrac{8-4\sqrt{2}+2\sqrt{2}}{8-4\sqrt{2}-2\sqrt{2}} \\ & = \dfrac{10-4\sqrt{2}}{6-4\sqrt{2}} - \dfrac{8-2\sqrt{2}}{8-6\sqrt{2}} \\ & = \dfrac{5-2\sqrt{2}}{3-2\sqrt{2}} - \dfrac{4-\sqrt{2}}{4-3\sqrt{2}} \\ & = \dfrac{(5-2\sqrt{2})(3+2\sqrt{2})}{9-8} - \dfrac{(4-\sqrt{2})(4+3\sqrt{2})}{16-18} \\ & = 15+4\sqrt{2} - 8 + \dfrac{16 + 8\sqrt{2} - 6}{2} \\ & = 7 +4\sqrt{2} + 5 + 4\sqrt{2} \\ & = 12+8\sqrt{2} \end{split} \end{equation} \)
Log in to reply
Err, sir, There is a typo in the line of the answer. It should be "+"
Log in to reply
Thanks.
Log in to reply
\(\huge\ddot\smile\)
Log in to reply
12+10\sqrt{2}
Log in to reply
@Soumya Khurana , I am afraid that there is no such option in the paper I got this from.
Log in to reply
Can u tell me the options @Mehul Arora
Log in to reply
Sure. a. \(12+ \sqrt {2}\)
b. \(12- \sqrt {2}\)
c. 2
d. -2
Log in to reply
@Mehul Arora , I am afraid that there is no such option in the paper which is the correct value of the expression above.
Log in to reply
There should be one more option as "None of the given". :P
Log in to reply
Yeah... I calculated it manually. :P
Log in to reply
Thanks! I just got juggled up with the signs.
\(cheers!\)
Log in to reply
@Mehul Arora I checked for sure using a claculator...None of the options match. :(
Log in to reply
Please see the explanation,
According to the question, we have to find,
\[\huge \dfrac{8-4\sqrt{2}+2}{8-4\sqrt{2}-2}-\dfrac{8-4\sqrt{2}+2\sqrt{2}}{8-4\sqrt{2}-2\sqrt{2}} \\ \huge =\dfrac{10-4\sqrt{2}}{6-4\sqrt{2}} \times \dfrac{6+4\sqrt{2}}{6+\sqrt{2}} - \dfrac{8-2\sqrt{2}}{8-6\sqrt{2}} \times \dfrac{8+6\sqrt{2}}{8+6\sqrt{2}} \\ \huge = 7+4\sqrt{2}-(-5-4\sqrt{2}) \\ \huge = \boxed{12+8\sqrt{2}} \]
Log in to reply
You have made a mistake.Find it.
Log in to reply
Simply put the value of \(a\) and calculate. :P
Log in to reply
The answer I am getting is \(12 + 8\sqrt{2}\) , Is it correct?
Log in to reply
The correct ans is \(12+8\sqrt{2}\).
Log in to reply
Yes , I am correct then. :P
Log in to reply
Yeah. Thank you sir. :)
I needed the answer. I found out the procedure.
Thanks everyone @Nihar Mahajan @Sravanth Chebrolu @Soumya Khurana and of course @Sandeep Bhardwaj sir.
Log in to reply
No need to @Mention!!! \(\huge \ddot \smile\)
Log in to reply
ha ha componendo dividendo solved it for me isnt that way easier???
Log in to reply
How did you solve this using componendo dividendo ? Also , post your solution.
Log in to reply
sorry i cant dont know a thing about latex.
Log in to reply
You can post a solution without latex too. I will understand it. Or at least post your approach.I am curious about this method.
Log in to reply