Waste less time on Facebook — follow Brilliant.
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
2 years, 5 months ago
No vote yet
1 vote
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
The correct ans is \(12+8\sqrt{2}\).
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
Yes , I am correct then. :P
Log in to reply
The answer I am getting is \(12 + 8\sqrt{2}\) , Is it correct?
Log in to reply
Simply put the value of \(a\) and calculate. :P
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
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
@Mehul Arora I checked for sure using a claculator...None of the options match. :(
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
Thanks! I just got juggled up with the signs.
\(cheers!\)
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
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