Mehul's doubt.

If $a=8-4\sqrt{2}$ then find the value of :

$\dfrac{a+2}{a-2} - \dfrac{a+2\sqrt{2}}{a-2\sqrt{2}}$

#Algebra

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> 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"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Sort by:

Top Newest

$\begin{aligned} \dfrac{a+2}{a-2} - \dfrac{a+2\sqrt{2}}{a-2\sqrt{2}} & = \dfrac{8-4\sqrt{2}+2}{8-4\sqrt{2}-2} - \dfrac{8-4\sqrt{2}+2\sqrt{2}}{8-4\sqrt{2}-2\sqrt{2}} \\ & = \dfrac{10-4\sqrt{2}}{6-4\sqrt{2}} - \dfrac{8-2\sqrt{2}}{8-6\sqrt{2}} \\ & = \dfrac{5-2\sqrt{2}}{3-2\sqrt{2}} - \dfrac{4-\sqrt{2}}{4-3\sqrt{2}} \\ & = \dfrac{(5-2\sqrt{2})(3+2\sqrt{2})}{9-8} - \dfrac{(4-\sqrt{2})(4+3\sqrt{2})}{16-18} \\ & = 15+4\sqrt{2} - 8 + \dfrac{16 + 8\sqrt{2} - 6}{2} \\ & = 7 +4\sqrt{2} + 5 + 4\sqrt{2} \\ & = 12+8\sqrt{2} \end{aligned}$

Chew-Seong Cheong - 5 years, 5 months ago

Err, sir, There is a typo in the line of the answer. It should be "+"

Mehul Arora - 5 years, 5 months ago

12+10\sqrt{2}

Soumya Khurana - 5 years, 5 months ago

@Soumya Khurana , I am afraid that there is no such option in the paper I got this from.

Mehul Arora - 5 years, 5 months ago

Can u tell me the options @Mehul Arora

Soumya Khurana - 5 years, 5 months ago

@Soumya Khurana – Sure. a. $12+ \sqrt {2}$

b. $12- \sqrt {2}$

c. 2

d. -2

Mehul Arora - 5 years, 5 months ago

@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 - 5 years, 5 months ago

@Nihar Mahajan – There should be one more option as "None of the given". :P

Sandeep Bhardwaj - 5 years, 5 months ago

@Sandeep Bhardwaj – Yeah... I calculated it manually. :P

Nihar Mahajan - 5 years, 5 months ago

@Nihar Mahajan – Thanks! I just got juggled up with the signs.

$cheers!$

Sravanth Chebrolu - 5 years, 5 months ago

@Mehul Arora – @Mehul Arora I checked for sure using a claculator...None of the options match. :(

Soumya Khurana - 5 years, 5 months ago

@Mehul Arora – Please see the explanation,

According to the question, we have to find,

$\huge \dfrac{8-4\sqrt{2}+2}{8-4\sqrt{2}-2}-\dfrac{8-4\sqrt{2}+2\sqrt{2}}{8-4\sqrt{2}-2\sqrt{2}} \\ \huge =\dfrac{10-4\sqrt{2}}{6-4\sqrt{2}} \times \dfrac{6+4\sqrt{2}}{6+\sqrt{2}} - \dfrac{8-2\sqrt{2}}{8-6\sqrt{2}} \times \dfrac{8+6\sqrt{2}}{8+6\sqrt{2}} \\ \huge = 7+4\sqrt{2}-(-5-4\sqrt{2}) \\ \huge = \boxed{12+8\sqrt{2}}$

Sravanth Chebrolu - 5 years, 5 months ago

@Sravanth Chebrolu – You have made a mistake.Find it.

Nihar Mahajan - 5 years, 5 months ago

Simply put the value of $a$ and calculate. :P

Sandeep Bhardwaj - 5 years, 5 months ago

The answer I am getting is $12 + 8\sqrt{2}$ , Is it correct?

Nihar Mahajan - 5 years, 5 months ago

The correct ans is $12+8\sqrt{2}$ .

Sandeep Bhardwaj - 5 years, 5 months ago

Yes , I am correct then. :P

Nihar Mahajan - 5 years, 5 months ago

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.

Mehul Arora - 5 years, 5 months ago

No need to @Mention!!! $\huge \ddot \smile$

Sravanth Chebrolu - 5 years, 5 months ago

ha ha componendo dividendo solved it for me isnt that way easier???

Kaustubh Miglani - 4 years, 10 months ago

How did you solve this using componendo dividendo ? Also , post your solution.

Nihar Mahajan - 4 years, 10 months ago

sorry i cant dont know a thing about latex.

Kaustubh Miglani - 4 years, 10 months ago

@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.

Nihar Mahajan - 4 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$