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0<b<a0<b<a0<b<a
a2+b2=6aba^{2}+b^{2}=6aba2+b2=6ab
What is the value of a−ba+b \dfrac{a-b}{a+b}a+ba−b?
As shown above, three identical ellipses of the minor axis 222 are positioned, such that each of them has four points of tangency with the regular hexagon at two opposite …
In the rectangular plane, let A,B,C,D,EA, B, C, D, EA,B,C,D,E be points, such that
The sequence {a1,a2,a3,… }\{a_1, a_2, a_3, \dots \}{a1,a2,a3,…} is defined by a2n+1=(−1)na_{2n + 1} = (-1)^na2n+1=(−1)n and a2n=ana_{2n} = a_na2n=an. A point PPP moves on the coordinate plane as follows.
2020,⌊α⌋,⌊β⌋,4040,⌊2α⌋,⌊2β⌋,6060,⌊3α⌋,⌊3β⌋,…2020, \lfloor \alpha \rfloor, \lfloor \beta \rfloor, 4040, \lfloor 2\alpha \rfloor, \lfloor 2\beta\rfloor, 6060, \lfloor 3\alpha \rfloor, \lfloor 3\beta\rfloor, \dots2020,⌊α⌋,⌊β⌋,4040,⌊2α⌋,⌊2β⌋,6060,⌊3α⌋,⌊3β⌋,…
Do there exist two positive real numbers α\alphaα and β\betaβ, …
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