New user? Sign up
Existing user? Log in
If a=8−42a=8-4\sqrt{2}a=8−42 then find the value of :
a+2a−2−a+22a−22 \dfrac{a+2}{a-2} - \dfrac{a+2\sqrt{2}}{a-2\sqrt{2}}a−2a+2−a−22a+22
Note by Nihar Mahajan 4 years, 1 month ago
</code>...<code></code> ... <code></code>...<code>."> Easy Math Editor
*italics*
_italics_
**bold**
__bold__
- bulleted- list
1. numbered2. list
paragraph 1paragraph 2
paragraph 1
paragraph 2
[example link](https://brilliant.org)
> This is a quote
This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"
2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Sort by:
a+2a−2−a+22a−22=8−42+28−42−2−8−42+228−42−22=10−426−42−8−228−62=5−223−22−4−24−32=(5−22)(3+22)9−8−(4−2)(4+32)16−18=15+42−8+16+82−62=7+42+5+42=12+82 \begin{aligned} \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{aligned} a−2a+2−a−22a+22=8−42−28−42+2−8−42−228−42+22=6−4210−42−8−628−22=3−225−22−4−324−2=9−8(5−22)(3+22)−16−18(4−2)(4+32)=15+42−8+216+82−6=7+42+5+42=12+82
Log in to reply
Err, sir, There is a typo in the line of the answer. It should be "+"
Thanks.
@Chew-Seong Cheong – ⌣¨\huge\ddot\smile⌣¨
12+10\sqrt{2}
@Soumya Khurana , I am afraid that there is no such option in the paper I got this from.
Can u tell me the options @Mehul Arora
@Soumya Khurana – Sure. a. 12+212+ \sqrt {2}12+2
b. 12−212- \sqrt {2}12−2
c. 2
d. -2
@Mehul Arora – @Mehul Arora , I am afraid that there is no such option in the paper which is the correct value of the expression above.
@Nihar Mahajan – There should be one more option as "None of the given". :P
@Sandeep Bhardwaj – Yeah... I calculated it manually. :P
@Nihar Mahajan – Thanks! I just got juggled up with the signs.
cheers!cheers!cheers!
@Mehul Arora – @Mehul Arora I checked for sure using a claculator...None of the options match. :(
@Mehul Arora – Please see the explanation,
According to the question, we have to find,
8−42+28−42−2−8−42+228−42−22=10−426−42×6+426+2−8−228−62×8+628+62=7+42−(−5−42)=12+82\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}} 8−42−28−42+2−8−42−228−42+22=6−4210−42×6+26+42−8−628−22×8+628+62=7+42−(−5−42)=12+82
@Sravanth Chebrolu – You have made a mistake.Find it.
Simply put the value of aaa and calculate. :P
The answer I am getting is 12+8212 + 8\sqrt{2}12+82 , Is it correct?
The correct ans is 12+8212+8\sqrt{2}12+82.
Yes , I am correct then. :P
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.
No need to @Mention!!! ⌣¨\huge \ddot \smile⌣¨
ha ha componendo dividendo solved it for me isnt that way easier???
How did you solve this using componendo dividendo ? Also , post your solution.
sorry i cant dont know a thing about latex.
@Kaustubh Miglani – You can post a solution without latex too. I will understand it. Or at least post your approach.I am curious about this method.
Problem Loading...
Note Loading...
Set Loading...
</code>...<code>."> 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 Newesta−2a+2−a−22a+22=8−42−28−42+2−8−42−228−42+22=6−4210−42−8−628−22=3−225−22−4−324−2=9−8(5−22)(3+22)−16−18(4−2)(4+32)=15+42−8+216+82−6=7+42+5+42=12+82
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
⌣¨
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+2
b. 12−2
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,
8−42−28−42+2−8−42−228−42+22=6−4210−42×6+26+42−8−628−22×8+628+62=7+42−(−5−42)=12+82
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+82 , Is it correct?
Log in to reply
The correct ans is 12+82.
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!!! ⌣¨
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