Question

Va rog!!! Si un exercitiu e bun​

Answer 1

Răspuns:

Explicație pas cu pas:

2.

2+ 4 + 6 + 8 +.....+2014 + 2016 =

a1 = 2

an = 2016

r= 2

an = a1 + (n - 1)r

2016 = 2 + (n - 1)*2 = 2 + 2n - 2 = 2n

n = 2016 : 2 = 1008

Sn = n(a1 + an)/2

2+ 4 + 6 + 8 +.....+2014 + 2016 = 1008*(2 + 2016)/2 = 1008*2019/2 =

= 1008*1009

x^2 + 1008 = 1008*1009

x^2 = 1008*1009 - 1008 = 1008 (1009 - 1) = 1008*1008 = 1008^2

x1 = 1008; x2 = -1008

__________________

4.

x^2 + (x + 2)^2 + (x - 2)^2 = (x + 3)^2 + (x - 3)^2 + 6

x^2 + x^2 + 4x + 4 + x^2 - 4x + 4 = x^2 + 6x + 9 + x^2 - 6x + 9 + 6

3x^2 + 8 = 2x^2 + 24

3x^2 - 2x^2 = 24 - 8

x^2 = 16

x1 = 4; x2 = -2