Question

Calcular el valor numérico de:
A = (a + 1)2 + (b + 1)2 + 2ab - 1

Answer 1

Respuesta:

$A\:=\:\left(a\:+\:1\right)2\:+\:\left(b\:+\:1\right)2\:+\:2ab\:-\:1$

$\left(a+1\right)\cdot \:2+\left(b+1\right)\cdot \:2+2ab-1-\left(b+1\right)\cdot \:2=A-\left(b+1\right)\cdot \:2$

$\left(a+1\right)\cdot \:2+2ab-1=A-\left(b+1\right)\cdot \:2$

$\left(a+1\right)\cdot \:2+2ab-1+1=A-\left(b+1\right)\cdot \:2+1$

$\left(a+1\right)\cdot \:2+2ab=-2b+A-1$

$2a+2+2ab=-2b+A-1$

$2a+2ab=-2b+A-3$

$2a+2ab=2a\left(1+b\right)$

$\boxed{2a\left(1+b\right)=-2b+A-3}$

Dividimos ambos lados entre 2(1 + b)

$\frac{2a\left(1+b\right)}{2\left(1+b\right)}=-\frac{2b}{2\left(1+b\right)}+\frac{A}{2\left(1+b\right)}-\frac{3}{2\left(1+b\right)}$       ⇒     $b\ne \:-1$

$\boxed{a=\frac{-2b+A-3}{2\left(1+b\right)}}$

Saludos...