if α and β are the roots of 4x^(2 ) −6x+1===00====================== =0. find α^3 −β^3 .


Question and Answers Forum

All Questions Topic List
None Questions
Previous in All Question Next in All Question
Previous in None Next in None
Question Number 63399 by smartsmith459@gmail.com last updated on 03/Jul/19

$i f α a n d β a r e t h e r o o t s o f 4 x^{2} - 6 x + 1 === 00 ======================$ $= 0 . f i n d α^{3} - β^{3} .$
Commented by mr W last updated on 03/Jul/19

$α + β = \frac{6}{4} = \frac{3}{2}$ $α β = \frac{1}{4}$ ${(α - β)}^{2} = {(α + β)}^{2} - 4 α β$ $\Rightarrow (α - β) = \pm \sqrt{{(α + β)}^{2} - 4 α β}$ $α^{3} - β^{3}$ $= (α - β) (α^{2} + β^{2} + α β)$ $= (α - β) [{(α + β)}^{2} - α β]$ $= \pm \sqrt{{(α + β)}^{2} - 4 α β} [{(α + β)}^{2} - α β]$ $= \pm \sqrt{\frac{9}{4} - 1} [\frac{9}{4} - \frac{1}{4}]$ $= \pm 2 \sqrt{\frac{5}{4}}$ $= \pm \sqrt{5}$
	Answered by MJS last updated on 03/Jul/19

	$4 x^{2} - 6 x + 1 = 0 \Rightarrow x = \frac{3}{4} \pm \frac{\sqrt{5}}{4}$ $if α < β \Rightarrow α = \frac{3}{4} - \frac{\sqrt{5}}{4} \land β = \frac{3}{4} + \frac{\sqrt{5}}{4}$ $\Rightarrow α^{3} - β^{3} = - \sqrt{5}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum