Question

a,b si c sunt d.p.cu 2,3,5.Daca (a-b)la patrat+(b-c)la patrat+(c-a)la patrat=56,aflati a,b si c.

Answer 1

a,b,c d.p cu 2,3,5<=> a/2=b/3=c/5=k=> a=2k,b=3k,c=5k
(a-b)(a-b)+(b-c)(b-c)+(c-a)(c-a)=56
a-b=2k-3k=-k
b-c=3k-5k=-2k
c-a=5k-2k=3k
orice numar la patrat este un un numar poziti=>
(a-b)(a-b)+(b-c)(b-c)+(c-a)(c-a)=1k patrat+4k patrat +9k patrat=14k patrat=56 => k patrat=4 => k=2 =>a=4,b=6,c=10