Nice But I think that my approach is faster (you don't need to multiply stuff).
Nice But I think that my approach is faster (you don't need to multiply stuff).
Here's a 3rd grade one. For 3 straight lines of length a = 3, b = 8, c = 7, prove that they can be used to form a triangle. Don't draw the triangle.
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The triangular inequality is one of the most useful in math and has been proven in many ways. It is commonly expressed as (regardless of which side is chosen to be a,b,c) |a-b|<c<a+b. The first part is added so that you won't need to check individually all three arrangements for c<a+b; this is equivalent to the former being true for any one arrangement. For example, in your case (3,6,7) we instead select b=3,a=7, c=8 and check if |7-3|<8<7+3, which is true=>these form a triangle.
Juxtapose to having (say) the numbers 1,2,6, which don't: |1-6|=5<2<7, the first part is false, likewise the second part false with |1-2|=1<5<3 and likewise the first part false with |2-6|=4<1<7. If you only used c<a+b, you have to run it by all cases instead of a random one.
Correct. I would have taken "the sum of any 2 sides is larger than the 3rd". Feel free to post the next one. I can't rep you yet though.
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NP, nor can I yet
Hm, I am not sure what I should post. They all are at the border between end of middle-school and early highschool level, although variations can be late highschool.
Ok, let's try this:
Prove that if a,b,c are sides of cubes (measured in meters), and if a+b+c=0, the volume of those three cubes (meaning a^3+b^3+c^3) will be 3abc (cubic meters).
(this is a famous identity)
note: for a+b+c=0, clearly they cannot all be positive numbers. You can imagine an emptying cube and some full ones, if you wish, but really this is meant to be solved with algebra and can be simply stated as "prove that if a+b+c=0, then a^3+b^3+c^3=3abc".
hint:
Spoiler Alert, click show to read:
Also, don't be sad/nervous if you don't find it. I can't account for how hard it may be, given I first saw the formula, not established it myself.
As for the quiz, it likely is too hard, so I will wait another day and then (if no one posts the answer or that they wish to keep trying) I will reveal the answer
Ok!
It was Euler's identify for the sum of three cubes. Which can be written as follows:
a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)
If you do the multiplication in the second part, you will see that you arrive at the first part.
Open floor!
Ok, here is a not complicated but also not "duh" easy question (it could be a fine question in a mid-highschool test, I suppose, and it certainly must have been posed there many times).
Prove that the x coordinate of the vertex of a parabola (ie of a polynomial of type ax^2+bx+c, with a not zero), equals -b/2a.
You can use what way you wish*, provided it is generalized. Personally I was thinking of an algebraic one and - in my case - the starting point was distance between the polynomial's roots (not all such polynomials have real roots, but you can provide a way to transform them to corresponding ones that have).
(the question is not "duh" also because often school-math teachers only feed the kids formulas, so the kids end up being unable to have any way to tell why the formulas stand ^^)
*I feel I should include one condition: you certainly shouldn't 'prove' this by using its sister formula (ie without proving that either ^^) for value of y at the vertex!
Hm, I fear that the above may have been also not helpful, if the thread is to actually have participation
Does anyone wish to post a new quiz?
Maybe I can try this, as a change of pace for the time being?
It's about general observation, you don't need to think of math functions.
Worth one more try? How about this one, which was posted at reddit Askmath (and is easy)
Edit:This is for n being an integer
for n integer, equal to or larger than 1. In math notation: for n E N*.
For n = any integer it's not. For n = 0 you get 9 + 1 - 4 - 1 = 5. For n = -1 you get 3 + 1/3 - 2 - 1/2 = 4/3 - 3/2 = -1/6
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You are right... It should work for n equal or over 1, though :o N<1 messes up the factorization.
Spoiler for my own proposed solution:
Spoiler Alert, click show to read: