Question

10. Determinati cifrele a, b, c, d in urmatoarele cazuri:
abcd+bcd+cd+d=7118​

Answer 1

Răspuns:

a = 6 ; b = 5 ; c = 3 ; d = 7

Explicație pas cu pas:

abcd+bcd+cd+d=7118​ <=>   a,b,c,d ≠ 0

1000a + 100b + 10c + d + 100b + 10c + d + 10c + d + d = 7118 <=>

1000a + 200b + 30c + 4d = 7118

i) 4d = 8  => d = 2

ii) 4d = 28 => d = 7

i) d = 2 => 1000a + 200b + 30c = 7118-8 = 7710  I:10 =>

100a+20b+3c = 771

3c = 21 => c = 7 =>

100a + 20b = 771-21 = 750   I:10 =>

10a + 2b = 75  => b ∉ N

ii) d = 7 => 1000a + 200b + 30c = 7118-28 = 7090  I:10 =>

100a + 20b + 3c = 709

3c = 9 => c = 3

100a + 20b = 709-9 = 700 I:20 =>

5a + b = 35 => a = 7 ; b = 0  nu convine  , b ≠ 0

                        a = 6 ; b = 5

abcd = 6537

6537+537+37+7 = 7118

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