Question

the equation x ^2+2x+2=0 has roots alpha and beta. then the value of alpha /15+ beta ^15​

Answer 1

${x}^{2} + 2x + 2 = 0 \\ {x}^{2} + 2x = - 2 \\ solving \: by \: completing \: the \: square \\ method \\ third \: term = {( \frac{1}{2} \times b)}^{2} = {( \frac{1}{2} \times 2)}^{2} \\ = {(1)}^{2} = 1 \\ adding \: 1 \: on \: both \: sides \\ \\ {x}^{2} + 2x + 1 = - 2 + 1 \\ {(x + 1)}^{2} = - 1 \\ (x + 1) = \sqrt{ - 1} = not\: defined \\ hence \: no \: real \: roots \: of \: the \: given \\ equation \: exist \\ hence \: for \: \alpha \: and \: \beta \: as \: roots \: of \: the \: {eq}^{n} \\ \frac{ \alpha }{15} + { \beta }^{15} = not \: defined$