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## Markd 3 years ago using a=-1, b=2, c=-3, d=4 show an expression using only those 4 letters that equals 22, 28 and 29. You can use square roots and exponents.

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1. theEric

Your teacher is maniacal, in that you can't use algebra to just solve or anything.... You could create a program to find the results of many, many combinations. But for now we'll just have to logic it out. Does that sound good? Or are you in a high level class that I'm not understanding?

2. theEric

Can we use addition and subtraction?

3. Markd

You can use addition or subtraction. it 7th grade math

4. theEric

like $z+z+z-y$

5. theEric

Okay, that makes this easier!

6. Markd

example: (b^d)-(a+c) = 20

7. theEric

Okay! Well I was going to be cheap, since you can really count with the -1. I mean, that's a. And -a = 1. So -a = 1, -a + -a =2, -a + -a + -a = 3, etc.

8. theEric

That's probably not the purpose of the assignment, though. Huh?

9. Markd

no, you can only use each number one time in each expression.

10. theEric

Oh! Tricky! :) A challenge!

11. Markd

another example -(d-c)^b/a = 14 note ^ means to the power

12. theEric

Understood, thank you!

13. theEric

And numbers are not allowed, right?

14. Markd

we had to come up with an expression for every day of the month of October. I got 28 of the 31 done and these last three have me stumped!

15. theEric

Oh wow!!

16. Markd

you can use the numbers -1, 2, -3 and 4 instead of the letters if you want to. you find the expression and the least I can do is translate it! lol

17. theEric

Haha, okay.

18. Markd

is this something you think you can help me with?

19. theEric

Haha, I'm working on it! Logically, it stinks that you can't use any more than once, but it's great that you can switch the sign of any of them by making them negative.

20. theEric

I need a break from some math homework of my own that's not due for a little while, so I'll work these out with you.

21. Markd

I kind of added the "switch the sign" rule myself. Im not sure that thats allowed but its the only way I could figure out some of them.

22. theEric

I see. This sounds like a tough math assignment.

23. Markd

Are you in high school or college?

24. theEric

25 = (b-c) ^ (d-a), so you can have that in case you're other one involved just making a variable negative. I'm in college. My brain is currently deflated... I was working on homework in a subject called, "Introduction to Mathematical Proofs". The premise of the class is that, if you know some basic math definitions, you can establish true statements. Everything in math is defined, very specifically. Example, even numbers. They have a definition. Pretty much, an even number is a multiple of 2. Then, (I won't bother you with details) and example of a truth you can mathematically prove is that the product of any two even numbers will be even. It's sort of common sense, but the course demands us to be very specific. Algebra makes it easier. Back to the 22, 28, and 29!

25. Markd

Sounds hard! But believe it our not i did understand what you just said!

26. theEric

Sweet! I believe it! The stuff you're working on is hard too!

27. Markd

Are you sure 25 is correct? (2--3)^4--1= 5^5 correct? isnt that 3,125?

28. Markd

am I wrong on my thinking?

29. theEric

Hahaha!! Umm...... Let's go with (2--3) * (4--1)

30. Markd

that works!

31. theEric

Haha, I did say my brain was deflated! Thank you for catching me, and I'm sorry I told you something incorrect!

32. Markd

its OK. your thinking was right

33. theEric

Haha, thank you.

34. Markd

this is kind of like the show "Are you smarter than a 6th grader"

35. theEric

Hahaha!! You are totally right!

36. theEric

Great comparison...

37. Markd

OK, we could use absolute value on 5 of these and I just found answers to 2 two of the ones I had already done without using absolute values. So I have 2 more I can use now. So if it helps you try using absolure values if you need to.

38. Markd

does that make sence?

39. Markd

example: |d|+|c|+|a|*b=16

40. theEric

Alright! Your assignment makes a point that there are a limited amount of absolute values. |a| = -a. Does your assignment want to limit that -a thing too? It's like (-1)a, which is involving another number... Maybe we can change them later, if you want!

41. Markd

of the 31 expression I can only have 5 that use absolute values. I have 2 more absolute values left to use. Keep in mind you can use as many absolute values you want to in each expression.

42. theEric

But then we can use -2 or -4 in multiplication so easily... They'd have to be multiplied by a = -1. Addition is fine. x + (-b) = x - b. Subtraction is also fine. x - (-b) = x + b

43. Markd

yes, I believe thate right. Im not sure I understood that.

44. theEric

Okay! I'm going to go to a store quickly. I'll be back.

45. Markd

ok

46. theEric

Well you weren't sure if we could just use -a, or -c. If we could, then why put a limit on how many absolute values we use? Since we can get the same result with -a as |a|, why put a limit on how many times we can use |a|, but not limit -a. I think -a would not count because you get -a by multiplying -1 and a. Since -1 is a number, it wouldn't be allowed.

47. Markd

i see your point.

48. theEric

-1, 2, -3, 4 Results by multiplying two different variables -2 = 2 * -1 3 = -3 * -1 -4 = 4 * -1 -6 = -3 * 2 8 = 4 * 2 -12 = 4 * -3 Results by using powers, but not absoute value 1 = 2 ^ -1 -1 = -3 ^ -1 1 = 4 ^ -1 16 = 4 ^ 2 81 = 4 ^ -3 Results by using powers, and possiblly absolute value 1 = 1 ^ 2 1 = 1 ^ 3 1 = 1 ^ 4 8 = 2 ^ 3 16 = 2 ^ 4 81 = 3 ^ 4

49. theEric

Haha, I don't know if that is helpful or not. But those are numbers you might recognize that you need. They are the result of taking two variables and doing something to them. I think I overcomplicated it :P

50. Markd

no, i follow you

51. theEric

Haha, alright.

52. theEric

Some of that is wrong, sorry.. I wrote a program to do that for me, so I wrote it wrong. 81 doesn't equal 4^-3

53. Markd

is 2^-1=-1 why wouldn't it be -2? Is that a rule?

54. theEric

Actually, ignore all of that! I made two mistakes: 1. Many of the second set are wrong because I switched.. like$4^{-1}\neq1$$(-1)^4=1$ 2. Some are wrong otherwise, as my program used a program that rounded. I didn't know that it would. Also, I didn't include all possibilities. Here are the powers, if you use two variables and possibly absolute value: 1 = 1 ^ 2 1 = 1 ^ 3 1 = 1 ^ 4 2 = 2 ^ 1 8 = 2 ^ 3 16 = 2 ^ 4 3 = 3 ^ 1 9 = 3 ^ 2 81 = 3 ^ 4 4 = 4 ^ 1 16 = 4 ^ 2 64 = 4 ^ 3

55. theEric

And obviously we won't worry about anything to the first power.... So here I took that out. 1 = 1 ^ 2 1 = 1 ^ 3 1 = 1 ^ 4 8 = 2 ^ 3 16 = 2 ^ 4 9 = 3 ^ 2 81 = 3 ^ 4 16 = 4 ^ 2 64 = 4 ^ 3

56. theEric

Do you really want to know how a negative power works? It's not that hard, but it doesn't give us any extra help here. I will show you, if you want.

57. Markd

no, its OK. I will work off of what you just sent

58. theEric

Okay! I just thought those numbers could help us possibly.

59. Markd

Dont forget we can also use square roots

60. theEric

Right, thanks!

61. theEric

If only we could reuse some..

62. Markd

Would be nice...

63. theEric

$\sqrt{4^{\left|-3\right|}}=\sqrt{64}=8$$\sqrt{\left|-3\right|^4}=\sqrt{81}=9$ More ways to get to 8 and 9, but maybe you already noticed! No use on focusing on what we can't do!

64. theEric

$8=2*4$$9=(-1)(-3)^2=\left|-3\right|^2$

65. Markd

can you think of anything that equals 20?

66. theEric

With or without absolute value?

67. Markd

(2^4)-(-1+-3) but that dont leave any numbers to use

68. Markd

either way

69. theEric

Right. I run into that problem too.

70. Markd

What state do you live in?

71. Markd

My brain is fried.

72. theEric

Understood. Maybe a break would help. And I hope you're not staying up too late! I don't know what time it would be where you are.

73. Markd

Im in Charlotte North Carolina. Its 11:40 here

74. theEric

Same here, in central Pennsylvania.

75. theEric

I'm not sure how dangerous it is to give town information over the internet. I'd presume it's not so bad. I never have though.

76. theEric

When is this project due?

77. Markd

Thank you so much for your help! It was a nice surprise to get your messages this morning.

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