Question

$\frac{a}{b} = \frac{c}{d} = \frac{e}{f} = k\\ \\\\Hallar : \frac{a^2+c^{2} +e^{2} }{ab+cd+ef}$

_a)1
b)k
c)1/k
d) $k^{2}$
e)k/2

Answer 1

Respuesta:

b) k

Explicación paso a paso:

a/b = c/d = e/f =k

a = b*k

c = d*k

e = f*k

= (a^2 + b^2 + e^2) / (ab + cd + ef)

= [ (b*k)^2 + (d*k)^2 + (f*k)^2] / [(b*k*b) + (d*k*d) + (f*k*f*)]

= [(b^2)*(k^2) + (d^2)*(k^2) + (e^2)*(k^2)] / [(b^2)*k + (d^2)*k + (f^2)*k]

= (k^2) * [b^2 + d^2 + f^2] / k*[b^2 + d^2 + f^2]

= k