Question

log2 ( x² + x + 2 ) =3

Answer 1

Resposta:

$log_{2}( {x}^{2} + x + 2 ) = 3 \\ log_{2}({x}^{2} + x + 2) = log_{2}( {2}^{3} ) \\ {x}^{2} + x + 2 = {2}^{3} \\ {x}^{2} + x + 2 = 8 \\ {x}^{2} + x - 6 = 0 \\ x = \frac{ - 1 + - \sqrt{1 - 4(1)( - 6)} }{2} \\ x = \frac{ - 1 + - \sqrt{1 + 24} }{2} \\ x = \frac{ - 1 + - \sqrt{25} }{2} \\ x = \frac{ - 1 + - 5}{2} \\ x = \frac{ - 1 + 5}{2} \\ ou \\ x = \frac{ - 1 - 5}{2} \\ x = 2 \: ou \: x = - 3 \\ \\ se \: x = 2 \\ log_{2}( {x}^{2} + x + 2) = 3 \\ log_{2}( {2}^{2} + 2 + 2) = 3 \\ log_{2}(8) = 3 \\ log_{2}( {2}^{3} ) = 3 \\ \\ 3 = 3 \\ \\ se \: x = - 3 \\ log_{2}( {x}^{2} + x + 2) = 3 \\ log_{2}( {( - 3)}^{2} + ( - 3) + 2) = 3 \\ log_{2}(9 - 1) = 3 \\ log_{2}(8) = 3 \\ log_{2}( {2}^{3} ) = 3 \\ 3 = 3$

logo a resposta é: x = 2 e x = -3