Question

Buna.

Fie 42/4a+3b fractie echiunitara si 3a+4b patrat perfect. Aflati a si b?
Multumesc

Answer 1

Răspuns:

(a,b)∈{(9,3), (8,2), (7,1)}

Explicație pas cu pas:

4a+3b=42, a,b∈{0,1,...,9}

3a+4b numar perfect

4a+3b=3a+4b+a-b=42

a-b<10,  a-b = 42 - (3a+4b)

3a+4b ∈ {36}, ⇒a-b=42-36=6,

variante posibile:  a-b= 6 = 9-3 = 8-2 = 7-1

⇒(a,b)∈{(9,3), (8,2), (7,1)}