Question

{a,b}direct proportionale cu {6,3} se stie ca a supra 2+b supra 2 =180
Aflati a=? ,b=?

Answer 1

{a,b} d.p {6,3}
a/ 2 + b/2 = 180
a/6= b /3 = k
a= 6k
b= 3k
6k /2 +3k/2 = 180
9k = 180
9k= 180 *2
9k = 360
k= 360:9
k= 40
a = 40*6= 240
b= 40*3 =120

Answer 2

[tex]\it \dfrac{a}{2}+\dfrac{b}{2} =\ ^{2)}180 \Longrightarrow a+b=360\ \ \ \ (*) \\\;\\ \\\;\\ \{a,\ b\} d.\ p.\ \{6,\ 3\} \Longrightarrow \dfrac{a}{6}=\dfrac{b}{3} =\dfrac{a+b}{6+3} \stackrel{(*)}{=} \dfrac{360}{9} =40[/tex]


[tex]\it \dfrac{a}{6} = 40 \Longrightarrow a=6\cdot40 \Longrightarrow a=240 \\\;\\ \\\;\\ \dfrac{b}{3} = 40 \Longrightarrow b=3\cdot40 \Longrightarrow b=120 [/tex]