Question

E(x)=(2x+1)²+(x-2)(x+2)-5(x²+1). a)Calculați E(1) b)=4(x-2). c) E(x)mai mic sau egal cu 18,x€R​

Answer 1

Răspuns:

Explicație pas cu pas:

E(x)=(2x+1)²+(x-2)(x+2)-5(x²+1)

a) E(1) = (2·1+1)²+(1-2)·(1+2)-5·(1²+1) = 9-3-10 = -4 =>

E(1) = -4

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b) E(x) = 4x²+4x+1+x²-4-5x²-5 = 5x²-5x²+4x-8 = 4x-8 = 4(x-2) =>

E(x) = 4(x-2)

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E(x) ≤ 18 <=> 4x-8 ≤ 18 <=> 4x ≤ 26  => x ≤ 26/4 => x ≤ 13/2 =>

x ∈ (-∞ ; 13/2]