Question

What is the most interesting math problem you've encountered that you could share? Post away!

Answer 1

Do you know how to prove all triangles are isosceles?

Answer 2

- the sum of two opposite sides and a diagonal of a quadrilateral is 20cm. The area of quadrilateral is 50cm^2. Find the length of the other diagonal.

this question is 100% correct and no information is missing :)

:D

Answer 3

Haha, that sounds surprisingly easy, but it's not..hmm

Answer 4

XD

Answer 5

My all time favorite math problem is a proof: The quadratic reciprocity law.

For distinct odd primes \(p,q\), show that
\[\large (p/q)(q/p)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}\]

(Gauss got so much obsessed with this problem and called it law )
https://en.wikipedia.org/wiki/Quadratic_reciprocity

Answer 6

*

Answer 7

@imqwerty Does the quadrilateral has to be convex?

Answer 8

Would this be a valid quadrilateral under the scope of that question?

Answer 9

its not given in the question so u can take any quadrilateral.

Answer 10

"the sum of two opposite sides and a diagonal of a quadrilateral is 20cm."

Which of the following is true?

one side + opposite side + diagonal = 20 cm; or,
one side + opposite side = diagonal = 20 cm

Answer 11

1st one

Answer 12

recently reasoning questions are fascinating

Answer 13

cool!

Answer 14

does it work with other integer or Z+ values?

Answer 15

the boxes for astro

Answer 16

nevermind, I just checked it myself

Answer 17

@mukushla is the answer emptyset ?

Answer 18

the given equation can be rearranged as

a^3 - b^3 = 199*200*ab
(a-b)(a^2+ab+b^2)=199*200*ab
(a-b)(a/b+b/a+1) = 199*200

since the right hand side is integer, it must be the case that a/b+b/a is also an integer

only integer value of a/b+b/a is 2 and this doesn't satisfy the equation, so there are no solutions