Răspuns:
1.
[tex]\frac{a}{4} =\frac{b}{3} =\frac{c}{5} =\frac{a+b+c}{4+3+5} =\frac{a+b+c}{12}[/tex]
[tex]\frac{a}{4}=\frac{a+b+c}{12}[/tex] ⇒ 12a=4a+4b+4c /:4
2a=b+c ⇒ b=2a-c
[tex]\frac{b}{3}=\frac{a+b+c}{12}[/tex] ⇒ 12b=3a+3b+3c /:3
3b=a+c
3(2a-c)=a+c
6a-3c=a+c
5a=4c (5,4)=1 ⇒ a=4, c=5
b=2·4-5 b=3
ab+bc+ca=37
4·3+3·5+5·4=12+15+20+37
2. [tex]\frac{x}{\frac{1}{\frac{1}{3} } } =\frac{y}{\frac{1}{\frac{1}{4} } } =\frac{z}{\frac{1}{\frac{1}{6} } } =\frac{x}{3} =\frac{y}{4} =\frac{z}{6} =\frac{x+y+z}{3+4+6}=\frac{36}{13}[/tex]
[tex]\frac{x}{3} =\frac{36}{13}[/tex]
13x=108 ⇒ [tex]x=\frac{108}{13}[/tex]
[tex]\frac{y}{4} =\frac{36}{13}[/tex]
13y=144 ⇒ [tex]y=\frac{144}{13}[/tex]
[tex]\frac{z}{6} =\frac{36}{13}[/tex]
13z=216 ⇒ [tex]z=\frac{216}{13}[/tex]
x+y+z=36
[tex]\frac{108}{13} +\frac{144}{13} +\frac{216}{13} =\frac{468}{13}=36[/tex]
3. [tex]\frac{a}{4} =\frac{b}{5} =\frac{c}{6} =\frac{a+b+c}{4+5+6} =\frac{75}{15}=5[/tex]
[tex]\frac{a}{4} =5[/tex] ⇒a=4·5 a=20
[tex]\frac{b}{5} =5[/tex] ⇒b=5·5 b=25
[tex]\frac{c}{6} =5[/tex] ⇒c=6·5 c=30
a+b+c=75
20+25+30=75
Explicație pas cu pas:
