Question

Dokończ rozwiązanie równania (1+x)+(2+3x)+(3+5x)+(4+7x)+...+(50+99x)=275

Answer 1

(100x+51)n=550
n=550/(100x+51)

50+99x=1+x+(n-1)(1+2x)
50+99x=1+x+[{550/(100x+51)} -1](1+2x)
49+98x= [(550-100x-51) / (100x+51)](1+2x)
49+98x= [(499-100x)(1+2x)] / (100x+51)
(49+98x)(100x+51)=499+998x-100x-200x²
4900x+2499+9800x²+4998x=-200x²+898x+499
10 000x²+ 9 000x + 2000=0
Δ=81 000 000 - 4*2 000* 10 000= 81 000 000 - 80 000 000 = 1 000 000
√Δ=1000
x1=(-9000+1000)/2* 10 000= - 8000/20 000 = -8/20 = -4/10 = -0,4
x2=(-9000 - 1000)/20 000= -10 000/20 000 = - 0,5

Answer 2