Question

(a,b,c,d) ip (2,3,4,6)
d-c+b-a=12
_______________
a,b,c,d=?

Answer 1

Explicație pas cu pas:

proporții derivate:

$\dfrac{a}{ \dfrac{1}{2} } = \dfrac{b}{ \dfrac{1}{3} } = \dfrac{c}{ \dfrac{1}{4} } = \dfrac{d}{ \dfrac{1}{6} } = \dfrac{d - c + b - a}{ \dfrac{1}{6} - \dfrac{1}{4} + \dfrac{1}{3} - \dfrac{1}{2} }$

$\dfrac{d - c + b - a}{ \dfrac{1}{6} - \dfrac{1}{4} + \dfrac{1}{3} - \dfrac{1}{2} } = \dfrac{12}{ \dfrac{2 - 3 + 4 - 6}{12}} = \dfrac{12}{ - \dfrac{3}{12}} = - 48$

$\dfrac{a}{ \dfrac{1}{2} } = \dfrac{b}{ \dfrac{1}{3} } = \dfrac{c}{ \dfrac{1}{4} } = \dfrac{d}{ \dfrac{1}{6} } = - 48$

$\dfrac{a}{ \dfrac{1}{2} } = - 48 \iff a = - \dfrac{48}{2} \implies a = - 24 \\ \dfrac{b}{ \dfrac{1}{3} } = - 48 \iff b = - \dfrac{48}{3} \implies b = - 16 \\ \dfrac{c}{ \dfrac{1}{4} } = - 48 \iff c = - \dfrac{48}{4} \implies c = - 12 \\ \dfrac{d}{ \dfrac{1}{6} } = - 48 \iff d = - \dfrac{48}{6} \implies d = - 8$