Question

Se dau numerele naturale a,b,c,d astfel incat b=2a, 3b=2c, 4c=3d.
a) Stabiliti daca b² =ad;
b) Aflati a,b,c,d stiind ca a+b+c+d=48

Answer 1

Stim ca b=2a, 3b=2c, 4c=3d.
a)
ad=$\frac{b}{2} * \frac{4c}{3}$  =  $\frac{b}{2} * \frac{4}{3} * \frac{3b}{2}$  = b²

b)a+b+c+d=48

c= $\frac{3b}{2}$ =  $\frac{3}{2} *$2a = 3a

d=$\frac{4}{3} c$=$\frac{4}{3} * \frac{3}{2}$*b=2b=4a

=>a+ 2a+3a+4a=48
10a=48
a=4.8
b=9.6
c=14.4
d=19.2