Найдите корень уравнения (x+5) + (2x+8) + (3x+11) + ... + (21x+65) = 1659

(x+2x+3x + ... + 21x) + (5+8+11 + ... + 65) = 1659;

(1+2+3 + ... + 21) x+21·2 + (3+6+9 + ... + 63) = 1659;

(21·22x) / 2+42+3 (1+2+3 + ... + 21) = 1659;

21·11x+3·21·11=1617;

3·7·11 (x+3) = 3·539;

7·11 (x+3) = 539;

11 (x+3) = 77;

x+3=7;

x=4

Ответ: 4

(x+5) + (2x+8) + (3x+11) + ... + (21x+65) = 1659

(x+2x+3x + ... 21x) + (5+8+11 + ... + 65) = 1659

(x + (2x+21x) + (3x+20x) + ... + (11x+12x)) + (5 + (8+65) + (11+62) + ... (35+38)) = 1659

(x + (23x) * 10) + (5+73*10)) = 1659

231x + 735 = 1659

231x = 924

x = 4