Question

Rezolvaţi ecuația:
16x² = 2•1 +2•3 +2•5 +2•7 + ... +2 • 2015 +2•2017 +2•2019.​

Answer 1

Răspuns:

Explicație pas cu pas:

2•1 +2•3 +2•5 +2•7 + ... +2 • 2015 +2•2017 +2•2019 =

2•(1 + 3 + 5 + 7 + ....+ 2015 + 2017 + 2019)

________

1 + 3 + 5 + 7 + ....+ 2015 + 2017 + 2019

a1 = 1

an = 2019

r = 2

an = a1 + (n - 1)•r

Sn = n•(a1 + an)/2

2019 = 1 + (n - 1)•2 = 1 + 2•n - 2 = 2•n - 1

2•n = 2019 + 1 = 2020

n = 2020 : 2 = 1010

1 + 3 + 5 + 7 + ....+ 2015 + 2017 + 2019 = 1010•(1 + 2019)/2 = 1010•2020/2 =

1010•1010

____________

16x^2 = 2•1010•1010

x^2 = 2•1010•1010/16 = 2•(1010/4)^2

x1 = 1010√2/4 = 505√2/2

x2 = -505√2/2