Question

find 1/ alpha+1/beta and alpha square +beta square from x^2+x-1/2​

Answer 1

• 1/alpha+1/beta=2
• alpha square+beta square=2

${ \bold{ \underline {\underline{Step \: by \: step \: solution:}}}}$

${ \bold{ \underline {\underline{Given:}}}}$

The equation is x^2+x-1/2

${ \bold{ \underline {\underline{To \: find:}}}}$

• 1/alpha + 1/beta
• alpha square+beta square

${ \bold{ \underline {\underline{We \: know \: that:}}}}$

• The equation x^2+x-1/2, comparing with ax^2+bx+c.
• Sum of the roots, alpha + beta = -b/a= -1/1 = -1
• Product of the roots, (alpha)(beta)=c/a =-(1/2)/1 = -1/2

${ \bold{ \underline {\underline{Solution:}}}}$

1st one,

$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \alpha + \beta }{ \alpha \beta } \\ = \frac{ - 1}{ - \frac{1}{2} } = 2 \\ \implies \boxed{ \frac{1}{ \alpha } + {\frac{1}{ \beta } } = 2}$

2nd one,

${ (\alpha + \beta) }^{2} = { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta \\ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta )}^{2} - 2 \alpha \beta \\ = { (- 1)}^{2} - 2( - \frac{1}{2} ) \\ = 1 + \frac{2}{2 } \\ = 1 + 1 = 2 \\ \boxed{{( \alpha + \beta )}^{2} = 2}$

Hope it helps✌️

Answer 2

2 and 3 is the answer

Hope it helps you