given-that-are-the-roots-of-the-equation-3×2-x-5-0-from-the-equation-whose-roots-are-2-1-2-1-

Question Number 216355 by jikansamu last updated on 05/Feb/25

g i v e n t h a t φ, β a r e t h e r o o t s o f t h e e q u a t i o n 3 x 2 - x - 5 = 0 f r o m t h e e q u a t i o n w h o s e r o o t s a r e 2 φ - 1 / β, 2 β - 1 / φ

Commented by AntonCWX last updated on 05/Feb/25

P l e a s e m a k e s u r e t o h a v e y o u r q u e s t i o n t y p e d n e a t l y a n d i n q u a l i t y .

Answered by AntonCWX last updated on 05/Feb/25

φ + β = - \frac{- 1}{3} = \frac{1}{3}

φ β = - \frac{5}{3}

\frac{2 φ - 1}{β} + \frac{2 β - 1}{φ}

= \frac{4 φ β - (φ + β)}{φ β}

= \frac{4 (- \frac{5}{3}) - (\frac{1}{3})}{- \frac{5}{3}}

= \frac{21}{5}

\frac{2 φ - 1}{β} \times \frac{2 β - 1}{φ}

= \frac{4 φ β - 2 (φ + β) + 1}{φ β}

= \frac{4 (- \frac{5}{3}) - 2 (\frac{1}{3}) + 1}{- \frac{5}{3}}

= \frac{19}{5}

N e w e q u a t i o n :

x^{2} - \frac{21}{5} x + \frac{19}{5} = 0

5 x^{2} - 21 x + 19 = 0

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