Question

Fie relatia $\frac{a}{4}= \frac{b}{5}= \frac{c}{3}$=k,cu k ∈ N.
a)Aratati ca:a²+c² este patrat perfect
b)Determinati a,b si c,stiind ca a+b+c=36

Answer 1

5a=4b => a = 4b/5
3b=5c => c = 3b/5

a. 16b²/ 25 + 9b²/25 = 25b² /25 = b² => e patrat perfect
b. 4b/5 + b + 3b/5 = 36
4b + 5b + 3b = 180
12b = 180 => b = 15 ; a= 12 ; c= 9