Find all the solutions to the equation 2u4 plus 38u2 equals 16u3 plus 24u?

Answer 1

2u4 + 38u2 = 16u3 + 24u

∴ u3 - 8u2 + 19u - 12 = 0

∴ (u - 3)(u2 - 5u + 4) = 0

∴ (u - 3)(u - 4)(u - 1) = 0

∴ u ∈ {1, 3, 4}

* * *

Because u is a factor of both sides of the equation given,

u = 0 is also a solution.