Question

(a-2)+1/a+2=-1 then the value of (a+2)squar2+ 1/(a+2)squar2 is

Answer 1

solution:

given: a-2+1/a+2=-1,
to find:$(a-2)^2+1/(a+2)^2$

 a-1/a+2=-1,
 a-1=-1(a+2)
 a-1=-a-2
 a+a=-2+1
2a=-1
 a=-1/2.....(i)

$(a-2)^2+1/(a+2)^2$
[tex]=(a^2-4a+4+1)/(a^2+4a+4) [/tex]
$=(-1/2)^2-4(-1/2)+5/(-1/2)^2+4(-1/2)+4$
[tex]=(1/4+2+5)/(1/4-2+4) [/tex]
[tex]=(1/4+28/4)/(1/4+8/4) [/tex]
$=(1/4+7)/(1/4+2)$
=(1/4+28/4)/(1/4+8/4)
=(29/4)/(9/4)
=29/9