Question

find the solution of x^80+11x^40+10​

Answer 1

Answer:

${x}^{80} + 11 {x}^{40} + 10 = 0 \\ \\ let \: {x}^{40} = y \\ \\ so \\ \\ \rightarrow \: {y}^{2} + 11y + 10 = 0 \\ \\ \rightarrow \: {y}^{2} + y + 10y + 10 = 0 \\ \\ \rightarrow \: y(y + 1) + 10(y + 1) = 0 \\ \\ \rightarrow \: (y + 1)(y + 10) = 0 \\ \\ replacing \: y \: by \: {x}^{40} \\ \\ \rightarrow \:{ \pink{ ( {x}^{40} + 1)( {x}^{40} + 10) = 0 }}\\ \\ \\ if \: ( {x}^{40} + 1) = 0 \\ \\ {x}^{40} = - 1 \\ \\ \\ if \: ( {x}^{40} + 10) = 0 \\ \\ {x}^{40} = - 10$