Răspuns:
x ∈ {0 ; 1 ; 2}
Explicație pas cu pas:
4x² - 8x - 5 ≤ 0 ; x ∈ Z ; x = ?
4x² - 8x - 5 = 0 => x₁,₂ = [8 ± √(64 + 80)]/8
x₁,₂ = (8±√144)/8
x₁,₂ = (8±12)/8
x₁ = (8-12)/8 = -4/8 => x₁ = -1/2
x₂ = (8+12)/8 = 20/8 => x₂ = 5/2
f(-1) = 4·(-1)²-8(-1)-5 = 4+8-5 = 7
f(3) = 4·9-8·3-5 = 36-24-5 = 7
Semnul functiei:
x -∞ -1 -1/2 5/2 3 +∞
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f(x) + + + + + + + 0 - - - 0 + + ++ + + + + +
f(x) ≤ 0 <=> x ∈ [-1/2 ; 5/2] I x ∈Z =>
x ∈ {0 ; 1 ; 2}
