let-and-the-roots-of-x-3-2x-1-0-find-the-value-of-A-2-2-2-and-B-3-3-3-

Question Number 64066 by mathmax by abdo last updated on 12/Jul/19

l e t α, β a n d λ t h e r o o t s o f x^{3} + 2 x - 1 = 0 f i n d t h e v a l u e o f

A = α^{2} + β^{2} + λ^{2} a n d B = α^{3} + β^{3} + λ^{3} .

Answered by MJS last updated on 12/Jul/19

the solutions are

α = u + v

β = (- \frac{1}{2} - \frac{\sqrt{3}}{2} i) u + (- \frac{1}{2} + \frac{\sqrt{3}}{2} i) v

λ = (- \frac{1}{2} + \frac{\sqrt{3}}{2} i) u + (- \frac{1}{2} - \frac{\sqrt{3}}{2} i) v

A = 6 u v

B = 3 (u^{3} + v^{3})

u = \sqrt[3]{- \frac{q}{2} + \frac{\sqrt{3 (4 p^{3} + 27 q^{2}}}{18}}

v = \sqrt[3]{- \frac{q}{2} - \frac{\sqrt{3 (4 p^{3} + 27 q^{2}}}{18}}

A = - 2 p

B = - 3 q

p = 2

q = - 1

A = - 4

B = 3

Commented by mathmax by abdo last updated on 12/Jul/19

t h a n k y o u s i r m j s