a+b+c=101
a:b=3 rest 5
a=3b+5
a=3(5c+3)+5
a=15c+9+5
a=15c+14
b:c=5 rest 3
b=5c+3
15c+14+5c+3+c=101
21c+17=101
21c=101-17
21c=84
c=84:21
c=4
a=15×4+14
a=60+14
a=74
b=5×4+3
b=20+3
b=23
(a+b-25c)^(a+b+c)=
=(74+23-25×4)¹⁰¹=
=(74+23-100)¹⁰¹=
=(97-100)¹⁰¹= -3¹⁰¹
Răspuns: - 3¹⁰¹
Explicație pas cu pas:
a + b + c = 101
a : b = 3 rest 5 ⇒ a = 3 × b + 5 ⇒ a = 3 ×(5×c+3)+5 ⇒ a = 15×c+14
b : c = 5 rest 3 ⇒ b = 5 × c + 3
________________________
a + b + c = 101
(15×c+14)+(5×c+3)+c= 101
21 × c + 17 = 101
21 × c = 101 - 17
c = 84 : 21 ⇒ c = 4
b = 5 × 4 + 3 ⇒ b = 23
a = 3 × 23 + 5 ⇒ a = 74
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(a + b - 25 c )¹⁰¹ = (74 + 23 - 25 x 4 )¹⁰¹ = (-3)¹⁰¹ = -3¹⁰¹
