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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

Răspuns :

Cpw
Stim ca b=2a, 3b=2c, 4c=3d.
a)
ad=[tex] \frac{b}{2} * \frac{4c}{3} [/tex]  =  [tex] \frac{b}{2} * \frac{4}{3} * \frac{3b}{2} [/tex]  = b²

b)a+b+c+d=48

c= [tex] \frac{3b}{2} [/tex] =  [tex] \frac{3}{2} *[/tex]2a = 3a

d=[tex] \frac{4}{3} c[/tex]=[tex] \frac{4}{3} * \frac{3}{2} [/tex]*b=2b=4a

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

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