Question

O valor de
$5 {x}^{0} + 3 {x}^{ \frac{3}{4} } + 4 {x}^{ - 0.5}$

, quando X=16, é

a) 30
b) 33
c) 75
d) 215
e) 105​

Answer 1

Resposta:

$5 {x}^{0} + 3 {x}^{ \dfrac{3}{4} } + 4 {x}^{ - 0.5} = \\ \\ = 5 {x}^{0} + 3 \sqrt[4]{ {x}^{3} } + \dfrac{4}{ {x}^{0.5} } \\ \\ = 5 {x}^{0} + 3( \sqrt[4]{x} ) {}^{3} + \dfrac{4}{ {x}^{ \dfrac{1}{2} } } \\ \\ = 5 {x}^{0} + 3( \sqrt[4]{x} ) {}^{3} + \dfrac{4}{ \sqrt{x} } \times \dfrac{ \sqrt{x} }{ \sqrt{ {x}} } \\ \\ = 5 {x}^{0} + 3( \sqrt[4]{x} ) {}^{3} + \dfrac{4 \sqrt{x} }{x} \\ \\ 5(16) {}^{0} +3 ( \sqrt[4]{16} ) {}^{3} + \dfrac{4 \sqrt{16} }{16} \\ \\ = 5 ( 1) +3( 2 {}^{3} ) + \frac{4 \times 4}{16} \\ \\ = 5 + 24 + \dfrac{16}{16} \\ \\ = 29 + 1 \\ \\ = \boxed{\bf{\green{ 30}}} \\ \\ \boxed{Letra \: \bf{ \pink{a) \: 30}}} \\ \\ \boxed{\large{ \bf{ \underline{Bons \: Estudos!}}}}$