Question

Resolva as equações: d) An,2 + An−1,2 + An−2,2 = 20

Answer 1

An,2 + An−1,2 + An−2,2 = 20

n(n-1) + (n-1).(n-2) + (n-2).(n-3) = 20

n²-n + n²-3n+2 + n²-5n+6 - 20 = 0

3n² -9n -12 = 0. ===> :(3)

n² -3n -4 = 0

∆=9+16=25 => √∆=5

n' = -b+√∆/2a = 3+5/2 = 8/2 = 4 ✓