Japanese| A nice math Olympiad problem| Algebra| No calculator is allowed

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A Nice math Olympiad algebra question. A full and detailed tutorial. #matholympiad #algebra #simplification .

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Комментарии
Автор

3^2^5+3^2^2^2+3^2^3+3^2^2+3^2 1^1+1^2+3^1 23 (x ➖ 3x+2).

RealQinnMalloryu
Автор

Perfect. Love your teaching beautiful and sweet lady

francisamewode
Автор

= 9^(5) + 9^(4) + 9^(3) + 9^(2) + 9
= 9^(4 + 1) + 9^(4) + 9^(2 + 1) + 9^(2) + 9
= [9^(4) * 9^(1)] + 9^(4) + [9^(2) * 9^(1)] + 9^(2) + 9
= { 9^(4) * [9^(1) + 1] } + { 9^(2) * [9^(1) + 1] } + 9
= { 9^(4) * [9 + 1] } + { 9^(2) * [9 + 1] } + 9
= { 9^(4) * 10 } + { 9^(2) * 10 } + 9
= 10.[9^(4) + 9^(2)] + 9
= 10.[9^(2 + 2) + 9^(2)] + 9
= 10.[ { 9^(2) * 9^(2) } + 9^(2) ] + 9
= 10.[ 9^(2) * {9^(2) + 1} ] + 9
= 10.[ 81 * {81 + 1} ] + 9
= 10.[81 * 82] + 9
= 10.[(80 + 1).(80 + 2)] + 9
= 10.[80² + (2 * 80) + (1 * 80) + (1 * 2)] + 9
= 10.[6400 + 160 + 80 + 2] + 9
= 10.[6400 + 100 + 60 + 80 + 2] + 9
= 10.[6400 + 100 + 140 + 2] + 9
= 10.[6500 + 142] + 9
= 10.[6642] + 9
= 66420 + 9
= 66429

key_board_x
Автор

9
81
729
6561
59049

66429
Starting with 9 in row one just multiply the previous row by 9 and add up the five rows. Why complicate things?

williamcousins