Question

Aratati ca numarul N=(x^2+x) ((x^2+x+2)+1=patrat perfect

Answer 1

$N = ( {x}^{2} + x)( {x}^{2} + x + 2) + 1$

$Notam \: \: {x}^{2} + x \: \: cu \: a.$

${x}^{2} + x = a$

$N = a(a + 2) + 1$

$N = {a}^{2} + 2a + 1$

$N = {(a + 1)}^{2}$

$= > N = {( {x}^{2} + x + 1)}^{2}$

$=>N=p.p$