Question

(a ,b )=15 a+b =180 dederminati nr naturale a si b stiind ca indeplinesc dimultan conditiile

Answer 1

(A,B)=15 ; a+b=180 A=d×x B=d×y A+B = 180 (A,B) = 1 15×x + 15×y =180 15×(x+y) =180 X+Y =180÷15 X+Y =12 (X,Y) =1 => x = 7 ; y=5 sau x=5; y=7 a = d×x a = 15×7 a= 105 b = d×y b = 15× 5 b = 75 a= 15×5 a = 75 b= 15×7 b=105 X =1 X=11 Y =11 sau Y=1 a = d×x a = 15×11 a = 165 b = d×y b = 15×1 b = 15 a = 15×1 a=15 b=15×11 b=165 (75;105) ; (105;75) ; (15;165) ; (165;15)