Point A is the intersection of y=x+α and y=2−x lines. ∴y=2−y+α ⇒2y=2+α ⇒y=‌
2+α
2
and x=2−‌
2+α
2
=‌
2−α
2
∴ Point A=(‌
2−α
2
,‌
2+α
2
) ∴AN = y-coordinate of point A=‌
2+α
2
Point B is the intersection of y=2+x and y=−x−α lines. ∴y=2−y−α ⇒2y=2−α ⇒y=‌
2−α
2
∴x=‌
2−α
2
−2=‌
2−α−4
2
=‌
−α−2
2
∴ Point B=(‌
−α−2
2
,‌
2−α
2
) ∴BM=y-coordinate of point B=‌
2−α
2
Area of the common region BRAE =∆CDE−(∆BCR+∆ARD) =‌
1
2
×4×2−(‌
1
2
(−α+2)×BM+‌
1
2
×(2+α)×AN) =4−(‌
1
2
×(2−α)×‌
(2−α)
2
+‌
1
2
×(2+α)×‌
2+α
2
) =4−[‌
(2−α)2
4
+‌
(2+α)2
4
] Given, 4−[‌
(2−α)2
4
+‌
(2+α)2
4
]=‌
3
2
⇒‌
(2−α)2
4
+‌
(2+α)2
4
=‌
5
2
⇒(2−α)2+(2+α)2=10⇒2α2+8=10 ⇒2α2=2 ⇒α2=1 ⇒α=±1 Given that α>0 so accepted value of α=+1. Now, 0≤y≤x+2α and |x|≤1 ⇒0≤y≤x+2‌ and ‌−1≤x≤1