a+a2+a3+(1/a)+(1/a2)+(1/a3)=28.Find the value of (2a-3)2
| No Solution Yet | Submitted by K Sengupta |
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With U = a + 1/a then
U^2 = a^2 + 2 + 1/a^2
U^3 = a^3 + 3U + 1/a^3
28 = (U^3 - 3U) + (U^2 - 2) + U
U^3 + U^2 - 2U - 30 = 0 = (U - 3)(U^2 + 4U +10)
The quadratic term has complex roots, I find that tiresome.
U = 3 gives a^2 - 3a + 1 = 0 with a = (3+- sqrt(5)) / 2 so
(2a -3)^2 = 5
Edited on November 12, 2024, 6:48 pm
| Posted by FrankM on 2024-11-12 18:47:25 |
