Question

Numerele naturale a , b si c sunt direct proportionale cu numerele 3,4 si respectiv ,5 . Sa se arate ca a²+b²=c²

Answer 1

[tex]\{a,b,c\} d.p.\{3,4,5\}=\ \textgreater \ \frac{a}{3}=\frac{b}{4}=\frac{c}{5}=k=\ \textgreater \ a=3k,b=4k,c=5k\\ a^2+b^2=c^2\\ (3k)^2+(4k)^2=(5k)^2\\ 9k^2+16k^2=25k^2\\ 25k^2=25k^2\\ 25=25(A)[/tex]

Answer 2

[tex]\frac{a}{3}=\frac{b}{4}=\frac{c}{5}=k\\\frac{a}{3}=k\to a=3k\\\frac{b}{4}=k\to b=4k\\\frac{c}{5}=k\to c=5k\\Demonstratie:\\a^{2}+b^{2}=c^{2}\\(3k)^{2}+(4k)^{2}=(5k)^{2}\\ 3^{2}k^{2}+(2^{2}k)^{2}=5^{2}k^{2}\\9k^{2}+(2^{2})^{2}k^{2}=25k^{2}\\ 9k^{2}+2^{2*2}k^{2}=25k^{2}\\9k^{2}+2^{4}k^{2}=25k^{2}\\9k^{2}+16k^{2}=25k^{2}\\ (9+16)k^{2}=25k^{2}\\25k^{2}=25k^{2}\\Adevarat!\\Sfarsit![/tex]