Question

Arătați că numărul N=...... este natural
$(x + 3) {}^{2} - 2x - (2 + x) {}^{2}$

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Answer 1

(x+3)²-2x-(2+x)²

x²+6x+9-2x-(4+4x+x²)

x²+6x+9-2x-4-4x-x²

6x+9-2x-4-4x

0+9-4

0+5

5=>numar.natural => € N

Answer 2

$N = {(x + 3)}^{2} - 2x - {(2 + x)}^{2}$

$N = {x}^{2} + 2 \times 3 \times x + {3}^{2} - 2x - ( {2}^{2} + 2 \times 2 \times x + {x}^{2} )$

$N = {x}^{2} + 6x + 9 - 2x - (4 + 4x + {x}^{2} )$

$N = {x}^{2} + 6x + 9 - 2x - 4 - 4x - {x}^{2}$

$N = {x}^{2} - {x}^{2} + 6x - 2x - 4x + 9 - 4$

$N = 5 \: \in \: \mathbb{N}$