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Mathematics
JAMB
Find the value of α
2
+ β
2
if α + β = 2 and the distance between points (1, α) and (β, 1)is 3 units
A.
14
B.
3
C.
5
D.
11
Correct Answer:
11
Explanation
PQ = √((β−1)
2
+(1−α)
2
). 3=√((β
2
−2β
2
+1+1−2α+α
2
)). 3=√((α
2
+β
2
−2α+2β+2)). 3=√((α
2
+β
2
−2(α+β)+2)). 3=√((α
2
+β
2
−2∗2+2)). 3=√((α
2
+β
2
−2)). 9=(α
2
+β
2
−2). α
2
+β
2
=9+2. α
2
+β
2
=11.
PQ = √((β−1)
2
+(1−α)
2
). 3=√((β
2
−2β
2
+1+1−2α+α
2
)). 3=√((α
2
+β
2
−2α+2β+2)). 3=√((α
2
+β
2
−2(α+β)+2)). 3=√((α
2
+β
2
−2∗2+2)). 3=√((α
2
+β
2
−2)). 9=(α
2
+β
2
−2). α
2
+β
2
=9+2. α
2
+β
2
=11.
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