Răspuns:
Explicație pas cu pas:
6)
a) 1 + 7 + 13 + ...+ x = 96
a1 = 1
an = x
r = 6
an = a1 + (n - 1)*r
x = 1 + (n - 1)*6 = 1 + 6n - 6 = 6n - 5
n = (x + 5)/6
Sn = n*(a1 + an)/2
96 = (x + 5)/6 * (1 + x)/2 = (x + 5)(x + 1)/12
(x + 5)(x + 1) = 96*12 = 1152
x^2 + x + 5x + 5 = 1152
x^2 + 6x + 5 - 1152 = 0
x^2 + 6x - 1147 = 0
Δ = 36 + 4588 = 4624 = 68^2
x = (-6 + 68)/2 = 62/2 = 31
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b)
-5 - 3 - 1 + 1 + 3 + 5 + 7 + 9 + ....+ x = 72
7 + 9 + ...+ x = 72
a1 = 7
an = x
r = 2
an = a1 + (n - 1)*r
x = 7 + (n - 1)*2 = 7 + 2n - 2 = 2n + 5
n = (x - 5)/2
Sn = n*(a1 + an)/2
72 = (x - 5)/2 * (7+ x)/2 = (x - 5)(x + 7)/4
(x - 5)(x + 7) = 72*4 = 288
x^2 + 7x - 5x - 35 = 288
x^2 + 2x - 35 - 288 = 0
x^2 + 2x - 323 = 0
Δ = 4 + 1292 = 1296 = 36^2
x = (-2 + 36)/2 = 34/2 = 17
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