Question

Toate trei va rog dau coroana

Answer 1

Răspuns:

1.

$\frac{a}{4} =\frac{b}{3} =\frac{c}{5} =\frac{a+b+c}{4+3+5} =\frac{a+b+c}{12}$

$\frac{a}{4}=\frac{a+b+c}{12}$ ⇒ 12a=4a+4b+4c   /:4

2a=b+c ⇒ b=2a-c

$\frac{b}{3}=\frac{a+b+c}{12}$ ⇒ 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. $\frac{x}{\frac{1}{\frac{1}{3} } } =\frac{y}{\frac{1}{\frac{1}{4} } } =\frac{z}{\frac{1}{\frac{1}{6} } } =\frac{x}{3} =\frac{y}{4} =\frac{z}{6} =\frac{x+y+z}{3+4+6}=\frac{36}{13}$

$\frac{x}{3} =\frac{36}{13}$

13x=108 ⇒ $x=\frac{108}{13}$

$\frac{y}{4} =\frac{36}{13}$

13y=144 ⇒ $y=\frac{144}{13}$

$\frac{z}{6} =\frac{36}{13}$

13z=216 ⇒ $z=\frac{216}{13}$

x+y+z=36

$\frac{108}{13} +\frac{144}{13} +\frac{216}{13} =\frac{468}{13}=36$

3. $\frac{a}{4} =\frac{b}{5} =\frac{c}{6} =\frac{a+b+c}{4+5+6} =\frac{75}{15}=5$

$\frac{a}{4} =5$ ⇒a=4·5    a=20

$\frac{b}{5} =5$ ⇒b=5·5    b=25

$\frac{c}{6} =5$ ⇒c=6·5    c=30

a+b+c=75

20+25+30=75

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