find 1/ alpha+1/beta and alpha square +beta square from x^2+x-1/2
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find 1/ alpha+1/beta and alpha square +beta square from x^2+x-1/2
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[tex]{ \bold{ \underline {\underline{Step \: by \: step \: solution:}}}}[/tex]
[tex]{ \bold{ \underline {\underline{Given:}}}}[/tex]
The equation is x^2+x-1/2
[tex]{ \bold{ \underline {\underline{To \: find:}}}}[/tex]
[tex]{ \bold{ \underline {\underline{We \: know \: that:}}}}[/tex]
[tex]{ \bold{ \underline {\underline{Solution:}}}}[/tex]
1st one,
[tex] \frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha \beta } \\ = \frac{ - 1}{ - \frac{1}{2} } = 2 \\ \implies \boxed{ \frac{1}{ \alpha } + {\frac{1}{ \beta } } = 2}[/tex]
2nd one,
[tex] { (\alpha + \beta) }^{2} = { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta \\ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta )}^{2} - 2 \alpha \beta \\ = { (- 1)}^{2} - 2( - \frac{1}{2} ) \\ = 1 + \frac{2}{2 } \\ = 1 + 1 = 2 \\ \boxed{{( \alpha + \beta )}^{2} = 2}[/tex]
Hope it helps✌️
2 and 3 is the answer
Hope it helps you