Question

determina numerele a,b,c stiind ca sunt invers proportionale cu 1 supra 2, 1 supra 7, 1 supra 5 si abc=1890 va rog repede ​

Answer 1

Răspuns:

$\boxed{\boxed{\bf \bigg(a;b;c \bigg) \in \bigg\{6;21;15 \bigg\} }}$

Explicație pas cu pas:

$\bf \bigg(a\,;b\,;c \bigg) \; i.p. \; \bigg( \; \dfrac{1}{2}\, ;\, \dfrac{1}{7} \,;\dfrac{1}{5} \,\bigg)$

$\bf a \cdot \dfrac{1}{2} = b\cdot \dfrac{1}{7} =c \cdot \dfrac{1}{5} =k$

$\bf \implies a \cdot \dfrac{1}{2}=k \implies a=k: \dfrac{1}{2} = 2k$

$\bf \implies b \cdot \dfrac{1}{7 } = k \implies b=k:\dfrac{1}{7} =7k$

$\bf \implies c \cdot \dfrac{1}{5} =k \implies c=k:\dfrac{1}{5} =5k$

$\bf \implies abc=1890 \implies a \cdot b \cdot c = 1890$

$\bf \implies 2k \cdot 5k\cdot 7 k = 1890$

$\bf \implies 70k^3 = 1890 \, | : 70 \implies k^3=27$

$\bf \implies k= \sqrt[\bf 3]{\bf 27} \implies \boxed{\bf k=3}$

$\bf a = 2k = 2 \cdot 3 \implies \boxed{\bf a = 6}$

$\bf b=7k=7\cdot 3 \implies \boxed{\bf b=21}$

$\bf c=5k = 5 \cdot 3 \implies \boxed{ \bf c = 15}$

Bafta! :)

#copaceibrainly

Answer 2

Răspuns:

a=6

b=21

c=15

Explicație pas cu pas:

a*1/2 =b*1/7=c*1/5=k

a= 2k,  b=7k,  c=5k

abc=1890

2k*7k*5k=1890

70$k^{3}$ =1890

$k^{3}$ = 1890/70, $k^{3}$=27,   k=$\sqrt[3]{27}$, k=3

a= 2k=2*3=6

b=7k= 7*3=21

c= 5k=5*3=15

Proba: abc= 6*21*15=1890 și 6*1/2=21*1/7=15*1/5 sau 3=3=3

#copaceibrainly