Question

Poate cineva sa ma ajute cu aceasta problema va rog , imi trebuie URGENT.Ofer 10p si Coroana. Multumesc

$\frac{ {2}^{2002} - {2}^{2001} - {2}^{2000} }{ {4}^{1001} } = \frac{x}{5}$

Answer 1

$\frac{ {2}^{2002} - {2}^{2001} - {2}^{2000} }{ {4}^{1001} } = \frac{x}{5} \\ \\ \frac{ {2}^{2000}( \frac{ {2}^{2002} }{ {2}^{2000} } - \frac{ {2}^{2001} }{ {2}^{2000} } - \frac{ {2}^{2000} }{ {2}^{2000} }) }{ { {(2}^{2}) }^{1001} } = \frac{x}{5} \\ \\ \frac{ {2}^{2000}( {2}^{2002 - 2000} - ( {2}^{2001 - 2000}) - 1) }{ {2}^{2 \times 1001} } = \frac{x}{5} \\ \\ \frac{ {2}^{2000}( {2}^{2} - 2 - 1) }{ {2}^{2002}} = \frac{x}{5} \\ \\ \frac{ {2}^{2000}(4 - 2 - 1) }{ {2}^{2002} } = \frac{x}{5} \\ \\ \frac{ {2}^{2000} }{ {2}^{2002} } = \frac{x}{5} \\ \\ \frac{1}{ {2}^{2002 - 2000} } = \frac{x}{5} \\ \\ \frac{1}{ {2}^{2} } = \frac{x}{5} \\ \\ 5 = 4x \\ \\ 4x = 5 \\ \\ \frac{4x}{4} = \frac{5}{4} \\ \\ x = \frac{5}{4}$