Question

O valor da expressão 1/a + 1/b para a+b=10 e ab=16, é:
a) 1/8
b) 1/16
c) 1/5
d) 5/8
e) 3/16

Answer 1

R: Letra D

veja

$\frac{1}{a} + \frac{1}{b} = \frac{b+a}{ab} = \frac{10}{16} = \frac{5}{8}$

Answer 2

$\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{b}{ab}+\dfrac{a}{ba}\\\\\\\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{b}{ab}+\dfrac{a}{ab}\\\\\\\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{b+a}{ab}$

Como b + a = 10 e ab = 16:

$\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{b+a}{ab}\\\\\\\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{10}{16}\\\\\\\boxed{\boxed{\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{5}{8}}}$

Letra D