Question

Exercițiul 3 va rog mult

Answer 1

a+b, b+c, c+a invers proportionale cu 0.(3), 0.25, 0.2.

Iar 0.(3)=1/3; 0.25=1/4; 0.2=1/5

Invers proportionalitate inseamna ca

(a+b)×(1/3)=(b+c)×(1/4)=(c+a)×(1/5).

Sau

(a+b)/3=(b+c)/4=(c+a)/5=k

a+b=3k

b+c=4k

c+a=5k

Adunam cele 3 ecuatii si obtinem

2(a+b+c)=12k

a+b+c=6k

Astfel obtinem:

a=2k, b=k, c=3k

Mai stim si ca: a^3×b^4×c^2=72

Adica: 8k^3×k^4×9k^2=72

72×k^9=72, k^9=2, deci k=1

Raspuns: numerele sint

a=2

b=1

c=3