Question

repede va rog,,dau 5 stele ​

Answer 1

Răspuns:

Explicație pas cu pas:

F(x) = (x³-3x²-x+3) / (x³-x²-9x+9)

a) x³-x²-9x+9 = 0 <=> x²(x-1) -9(x-1) = (x²-9)(x-1) = (x-3)(x+3)(x-1)

=> x ∈ R - {-3 ; 1 ; 3}

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b) F(1/2) = [(1/2)³-3·(1/2)²-1/2+3] / [(1/2)³-(1/2)²-9·(1/2)+9] =

= (1/8-²⁾3/4-⁴⁾1/2+⁸⁾3)/(1/8-²⁾1/4-⁴⁾9/2+⁸⁾9) =

= (1-6-4+24)/8 : (1-2-36+72)/8 =

= 15 / 35⁽⁵ = 3/7

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c) x³-3x²-x+3 = x²(x-3)-(x-3) = (x-3)(x²-1) = (x-3)(x-1)(x+1) =>

F(x) = [(x-3)(x-1)(x+1)] : [(x-3)(x+3)(x-1)]

se simplifica prin (x-3)(x-1) =>

F(x) = (x+1)/(x+3)