Question

[1+(1+2+2^2 +... 2^9)]×*=(2^3) ^4:2​

Answer 1

Vom calcula mai intai 1+2+2²+...+2⁹

$s = 1 + 2 + {2}^{2} + ... + {2}^{9} \\ 2s = 2 + {2}^{2} + {2}^{3} + ... + {2}^{10} \\ \implies \: s = 2s - s = 1 + {2}^{10}$

Deci acum vom inlocui 1+2+2²+...+2⁹ cu 1+2¹⁰

$[1 + (1 + {2}^{10} )] + x = ( {2}^{3} ) {}^{4} : 2 \\ 2 + {2}^{10} + x = {2}^{11} \\ 2 + x = {2}^{11} - {2}^{10} \\ 2 + x = {2}^{10} \\ x = {2}^{10} - 2 \\ x = 1024 - 2 \\\boxed{ x = 1022}$