find the equation whose roots are α and β. find α and β if α−β=2 and α^2 −β^2 =3


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Question Number 132358 by Engr_Jidda last updated on 13/Feb/21

$f i n d t h e e q u a t i o n w h o s e r o o t s a r e$ $α a n d β . f i n d α a n d β i f α - β = 2 a n d α^{2} - β^{2} = 3$
Commented by Dwaipayan Shikari last updated on 13/Feb/21

$x^{2} - (α + β) x + α β = 0 \Rightarrow x^{2} - \frac{3}{2} x + \frac{7}{16} = 0$ $(α - β) (α + β) = 3 \Rightarrow α + β = \frac{3}{2} \land α - β = 2$ $α = \frac{7}{4} β = - \frac{1}{4}$
Commented by Engr_Jidda last updated on 13/Feb/21

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