Question

Determine o valor de x, de modo que x², (x+1)² e (x+3)², nessa ordem, formem uma P.A..

Answer 1

$a_{1}=x^{2} \\ a_{2}=(x+1)^{2} \\ a_{3}=(x+3)^{2}$

$r = a_{2}-a_{1} \\ r=a_{3}-a_{2}$

$a_{2}-a_{1}=a_{3}-a_{2} \\ a_{2}+a_{2}=a_{3}+a_{1} \\\\ \boxed{\boxed{2*a_{2}=a_{1}+a_{3}}}$
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$2*a_{2}=a_{1}+a_{3} \\ 2*(x+1)^{2}=x^{2}+(x+3)^{2}$
$2*(x^{2}+2*x*1+1^{2})=x^{2}+(x^{2}+2*x*3+3^{2})$
$2*(x^{2}+2x+1)=x^{2}+x^{2}+6x+9$
$2x^{2}+4x+2=2x^{2}+6x+9 \\ 4x+2=6x+9 \\ 2-9=6x-4x \\ -7=2x \\ x=-7/2$