>>10830747The first one ends up becoming a Dirichlet integral.
bottle = 10, burger = 5, double glass = 2
integral from 0 to inf of sin(x)/5x dx = [pi/2]/5 = pi/10
The second one:
a/(b+p) + b/(a+p) + p/(a+b) = 4
a(a+p)(a+b) + b(b+p)(a+b) + p(b+p)(a+p) = 4(b+p)(a+p)(a+b)
(a^3 + a^2b + a^2p + abp) + (b^3 + ab^2 + b^2p + abp) + (p^3 + ap^2 + bp^2 + abp) = 4(a^2b + a^2p + ab^2 + 2abp + ap^2 + b^2p + bp^2)
a^3 + b^3 + p^3 - 3(a^2b + a^2p + ab^2 + b^2p + ap^2 + bp^2) - abp = 0
Clearly the answers are:
a=154476802108746166441951315019919837485664325669565431700026634898253202035277999,
b=36875131794129999827197811565225474825492979968971970996283137471637224634055579,
c=4373612677928697257861252602371390152816537558161613618621437993378423467772036
[spoiler:lit]Just kidding, I looked it up. Thinking of equations as manifolds is a bit past me for the moment.[/spoiler:lit]
