Thread: A problem I can't figure out at all!

Originally Posted by MutantJohn

Wait, if we have 3 equations with 3 unknowns, can't we just represent this as a linear system of equations?

You're right about the 3 equations and 3 unknowns, but the equations are quadratic not linear.

Code:

t * (t + 1) / 2 == p * (3 * p - 1) / 2 == h * (2 * h - 1)

or (using ** to mean "to the power of")

t**2 + t == 3*p**2 - p == 4*h**2 - 2*h

One of the math gurus here can tell us if this is solvable as a system of equations.

Originally Posted by oogabooga

You're right about the 3 equations and 3 unknowns, but the equations are quadratic not linear.

Code:

t * (t + 1) / 2 == p * (3 * p - 1) / 2 == h * (2 * h - 1)

or (using ** to mean "to the power of")

t**2 + t == 3*p**2 - p == 4 h**2 - 2 h

This could be written as 3 equations, 4 unkowns

t**2 + t == 2 s
3*p**2 - p == 2 s
4*h**2 - 2*h == 2 s

Some solutions for (h, p, t, s):
(0, 0, 0, 0)
(143, 165, 285, 40755)
(27693, 31977, 55385, 1533776805)
(5372251, 6203341, 10744501, 57722156241751)
(1042188953, 1203416145, 2084377905, 2172315626468283465)

Originally Posted by rcgldr

This could be written at 4 equations, 3 unkowns

t**2 + t == 2 s
3*p**2 - p == 2 s
4*h**2 - 2*h == 2 s

Solutions so far for (h, p, t, s) == (0, 0, 0, 0) , (143, 165, 285, 40755), (27693, 31977, 55385, 1533776805)

Arghh! You're right, I wasn't thinking.
Although it's 3 equations and 4 unknowns.