Buna .. Numerele naturale a,b,c  sunt d.p cu 2,3 si 5 . 
A )Cat la suta din numarul  c reprezinta numarul a?
b) Stiind ca (a-b)^2 +(b-c)^2+(c-a)^2=56 , aflati numerele a,b si9 c

Răspuns :

[tex]a) \frac{a}{2} = \frac{b}{3} = \frac{c}{5} =k=>a=2k;b=3k;c=5k\\ \frac{a}{2} = \frac{c}{5}=>a= \frac{2c}{5} =>a=\frac{40c}{100}=\frac{40}{100}\cdot c\\ a=40\%\ din\ c\\ [/tex]
[tex]b)(a-b)^2 +(b-c)^2+(c-a)^2=56\\ (2k-3k)^2+(3k-5k)^2+(5k-2k)^2=56\\ k^2+4k^2+9k^2=56\\ 14k^2=56\\ k^2=4\\ k=\pm \sqrt{4}=\pm2\\ k\in N=>k=2\\ a=2k=4\\ b=3k=6\\ c=5k=10 [/tex]

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