Question

if alpha and beta are the roots of the eqation x²-4x-6=0 then find alpha² +beta² and alpha³+beta³​

Answer 1

Answer:

${ \alpha }^{2} + { \beta }^{2} = 28. \\ \\ { \alpha }^{3} + { \beta }^{3} = - 8.$

Step-by-step explanation:

${x}^{2} - 4x + 6 = 0 \\ \\ \alpha + \beta = 4 \\ \\ \alpha \beta = - 6 \\ \\ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta) }^{2} - 2 \alpha \beta \\ \\ = {4}^{2} - 2( - 6) \\ \\ = 16 + 12 \\ \\ = 28. \\ \\ \\ \\ { \alpha }^{3} + { \beta }^{3} = {( \alpha + \beta) }^{3} - 3 \alpha \beta ( \alpha + \beta ) \\ \\ = {4}^{3} - 3( - 6)(4) \\ \\ = 64 - 72 \\ \\ = - 8.$