Question

alpha and bitta are roots of y^2-2y-7=0 find alpha ^2+bitta^2
​

Answer 1

${\huge{\underline{\underline{\mathfrak{\pink{A}\green{n}\blue{s}\red{w}\orange{e}\pink{r}}}}}}$

${y}^{2} - 2y - 7 = 0$

which root are

$\alpha$ and $\beta$

know that,

$\alpha + \beta = 2$

$\alpha \beta = - 7$

also know that,

$( {a + b})^{2} - 2ab = {a}^{2} + {b}^{2}$

$( {a + b})^{3} - 3ab(a + b) = {a}^{3} + {b}^{3}$

therefore,

${ \alpha }^{2} + { \beta }^{2} = {2}^{2} - 2 \times ( - 7) = 18$

${ \alpha }^{3} + { \beta }^{3} = {2}^{3} \times ( - 7) \times 2 = 8 + 42 = 50$