a)5.(x+3)-2.(x+4)-(x-2)=17
=> 5x + 15 - 2x - 8 - x + 2 = 17
=> 2x + 9 = 17
=> 2x = 8
=> x = 4
b) S=1.3+2.4+3.5+...+48.50+49.51
= 1(2 + 1) + 2(3 + 1) + 3(4 + 1) + ... + 48(49 + 1) + 49(50 + 1)
= 1 + 1.2 + 2 + 2.3 + 3 + 3.4 + ... + 48 + 48.49 + 49 + 49.50
= (1 + 2 + 3 + ... + 49) + (1.2 + 2.3 + 3.4 + ... + 49.50)
đặt A = 1 + 2 + 3 + ... + 49 = (1 + 49).49 : 2 = 1225
đặt B = 1.2 + 2.3 + 3.4 + ... + 49.50
3B = 1.2.3 + 2.3.3 + 3.4.3 + ... + 49.50.3
3B = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 49.50.(51 - 48)
3B = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 49.50.51 - 48.49.50
3B = 49.50.51
B = 49.50.51 : 3 = 41650
A + B = S = 41650 + 1225 = 42875