Question

Determinati numerele a si b stiind ca frectiile
21              3
------------ = --
(a+6)(b+1) 5
 
sunt egale

Answer 1

21/(a+6)(b+1) = 3/5⇒ (a+6)(b+1) = (5·21)/3 ⇒(a+6)(b+1 ) = 35

35 = 1·35 = 5·7 = 7·5 = 35·1

a+6 ∈ {1, 5, 7, 35} |-6 ⇒ a ∈ {-5, -1, 1, 29}

b+1 ∈ {35, 7, 5, 1} |-1 ⇒ b ∈ {34, 6, 4, 0}

(a, b) ∈ {(-5, 34), (-1, 6), (1, 4), (29, 0)}