Question

Sendo f(x)= √3 x² + 3x - √3, calcular:b-) f(3) - f(√3)/ √3 + 3

Answer 1

Primeiro calcularemos $f(3)$ e $f( \sqrt{3} )$:

$f(x) = x^2\sqrt{3} + 3x - \sqrt{3} \\ \\ f(3) = (3)^2 \sqrt{3} + 3*(3) - \sqrt{3 } \\ f(3) = 9 \sqrt{3} + 9 - \sqrt{3} \\ f(3) = 8 \sqrt{3} + 9 \\ \\ f( \sqrt{3} ) = (\sqrt{3}) ^2 \sqrt{3} + 3*( \sqrt{3} ) - \sqrt{3} \\ f( \sqrt{3} ) = 3 \sqrt{3} + 3 \sqrt{3} - \sqrt{3} \\ f( \sqrt{3} ) = 5 \sqrt{3}$

Logo temos:

$= \frac{f(3) - f( \sqrt{3} )}{ \sqrt{3} + 3 } \\ \\ = \frac{(8 \sqrt{3} + 9 ) - 5 \sqrt{3} }{ \sqrt{3} + 3 } \\ \\ = \frac{3 \sqrt{3} + 9 }{ \sqrt{3} + 3 } \\ \\ = \frac{3( \sqrt{3} + 3) }{ \sqrt{3} + 3} \\ \\ = 3$