Question

Exercițiul 2
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Answer 1

1. 1/(√1 +√2) +1/(√2 +√3) +1/(√3 +√4) +...+1/(√99 +√100) =1/1 -1/√2 +1/√2 -1/√3 +...+1/√99 -1/10 =1 -1/10 = 9/10 ∈Q.

2. f:R⇒R, f(x) =x² -m·x +2

Graficul functiei f intersecteaza axa Ox in doua puncte diferite daca si numai daca Δ > 0 <=> b² -4·a·c > 0 <=> (-m)² -4·1·2 > 0 <=> m² -8 > 0 <=> m² > 8 => m ∈{-∞,-2√2) ∪ (2√2,+∞), adica S = {-∞,-2√2) ∪ (2√2,+∞).