Question

a raiz positiva da equação
$(x + {1})^{3} - (x - {1})^{3} = 50$
é:
$a)1 + \sqrt{2}$
$b)1 + \sqrt{3}$
$c)2 \sqrt{2}$
$d)2 \sqrt{3}$
$e)3 \sqrt{2}$
​

Answer 1

Resposta:

$c) \;x=2\sqrt{2}$

Explicação passo-a-passo:

$(x+1)^3-(x-1)^3=50\\\\x^3+3x^2+3x+1-(x^3-3x^2+3x-1)=50\\\\x^3+3x^2+3x+1 -x^3+3x^2-3x+1=50\\\\6x^2+2=50\\\\6x^2=50-2\\\\6x^2=48\\\\x^2=\frac{48}{6} \\\\x^2=8\\\\x=\pm\sqrt{8} \\\\x=\pm 2\sqrt{2}$

A raiz positiva é $x=2\sqrt{2}$