Question

Sirul a,b,c invers proportional cu 5 ,6,7
3abc=35(ab+bc+ac) cat e a,b,c

Answer 1

5a=6b=7c=k  deci:

a=$\frac{k}{5}$

b=$\frac{k}{6}$

c=$\frac{k}{7}$  si inlocuim in expresia data:

3abc=35(ab+bc+ac) si obtinem:

$\frac{3 k^{3} }{5*6*7} =35* k^{2} ( \frac{1}{5*6} + \frac{1}{6*7} + \frac{1}{5*7} )$  si inmultim ambii membri cu 5*6*7, impartind, totodata, la $k^{2}$:

3k=35*(7+5+6)
3k=35*18
k=210 deci:

a=$\frac{210}{5}$=42

b=$\frac{210}{6}$=35

c=$\frac{210}{7}$=30