Exercițiul 472

E.472. Dacă ab=ab+2,a \bigodot b = a-b+2, calculați [(97)3]2\big[\big(9 \bigodot 7\big) \bigodot 3\big] \bigodot 2 și [9(73)]2.\big[9 \bigodot \big(7 \bigodot 3\big)\big] \bigodot 2.

Mate2000 pentru performanță, 17/18

Răspuns: 3,3, respectiv 5.5.

Soluție:

[(97)3]2=\big[\big(9 \bigodot 7\big) \bigodot 3\big] \bigodot 2=
[(97+2)3]2=\big[(9-7+2) \bigodot 3\big] \bigodot 2=
(43)2=(4 \bigodot 3) \bigodot 2=
(43+2)2=(4- 3+2) \bigodot 2=
32=32+2=3.3 \bigodot 2=3-2+2 = 3.

[9(73+2)]2=\big[9 \bigodot \big(7 -3 + 2\big)\big] \bigodot 2=
(96)2=(9 \bigodot 6) \bigodot 2=
(96+2)2=(9 - 6 + 2) \bigodot 2=
52=52+2=5.5 \bigodot 2= 5-2+2 = 5.