Each of a, b, and c is a real number that satisfy:
a-b = a*b*c
b-c = a*b*c
c+a = 3*a*b*c
Using only p&p, how fast can you come up with all possible values of a*c
Let abc=x
a-b=x, b-c=x, a+c=3x
Solutions: a=5c, b=3c.
Substitution:
2c=15c^3, 2=15c^2, c=+-sqrt(2/15),
and b=+-sqrt(30)/5, b=+-sqrt(6/5)
and a=+-sqrt(30)/3, a=+-sqrt(10/3)
The hardest part was simplifying the square roots for b and c, say 15 mins in all.
Note to self: next time, finish reading the problem before starting the clock.
Edited on June 22, 2024, 11:36 pm
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Posted by broll
on 2024-06-22 02:17:01 |
Possible Solution
