Question

qual o valor de :
a) Raiz de 123456^2+123456+123457

Answer 1

$\sqrt{123456^2+123456+123457} = \sqrt{123456^2+123456+123456+1} = \\ \sqrt{123456^2+2.123456+1} = \sqrt{(123456+1)^2}= \sqrt{123457^2} =123457$

Answer 2

Seja a = 123456
$\sqrt{123456^2+123456+123457} \\ = \sqrt{123456^2+123456+123456+1}\\ = \sqrt{a^2+a+a+1}\\ = \sqrt{a^2+2a+1}\\ = \sqrt{(a+1)^2}\\ = a+1$
como a =123456, temos que:
a + 1 = 123456 + 1 = 123457