Răspuns:
Explicație pas cu pas:
2) a₁ = 1 ; a₂ = 3 ; a₂ = a₁ + r =>
r = a₂-a₁ = 3-1 = 2
a₃ = a₂+r = 3+2 = 5 ; a₄ = a₃+r = 5+2 = 7 ;
a₅ = a₄+r = 7+2 = 9
S₅ = a₁+a₂+a₃+a₄+a₅ = 1+3+5+7+9 = >
S₅ = 25
3) f(x) = mx²-8x-3 ; f: R --> R
f max = 5 <=> mx²-8x-3 = 5 =>
mx² -8x+2 = 0 => x₁,₂ = [8 ±√(64-8m)]/2m
x = -b/2a ; a = m ; b = -8 ; c = 2
x = 8/2m = 4/m = >
[8 ±√(64-8m)]/2m = 8/2m =>
8 ±√(64-8m) = 8 =>
±√(64-8m) = 0 =>
64 - 8m = 0 => 8m = 64 => m = 8
