If alpha and beta are the roots of the equation x2+px+q=0, find the value of alpha^2+beta^2.
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Answer:
\alpha + \beta = pα+β=p
\alpha \beta = qαβ=q
1.
\: { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta )}^{2} - 2 \alpha \betaα
2
+β
2
=(α+β)
2
−2αβ
= {p}^{2} - 2q=p
2
−2q
2.
\frac{1}{ \alpha } + \frac{1}{ \beta }
α
1
+
β
1
= \frac{ \alpha + \beta }{ \alpha \beta }=
αβ
α+β
= \frac{p}{q}=
q
p
3.
\frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } = \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } = \frac{ {p}^{2} - 2q }{q}
β
α
+
α
β
=
αβ
α
2
+β
2
=
q
p
2
−2q
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