2004
Mathematics
67ca00ce0c643c71d77dee1f
Find the value of α2 + β2 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=√((β2−2β2+1+1−2α+α2)). 3=√((α2+β2−2α+2β+2)). 3=√((α2+β2−2(α+β)+2)). 3=√((α2+β2−2∗2+2)). 3=√((α2+β2−2)). 9=(α2+β2−2). α2+β2=9+2. α2+β2=11.
PQ = √((β−1)2+(1−α)2). 3=√((β2−2β2+1+1−2α+α2)). 3=√((α2+β2−2α+2β+2)). 3=√((α2+β2−2(α+β)+2)). 3=√((α2+β2−2∗2+2)). 3=√((α2+β2−2)). 9=(α2+β2−2). α2+β2=9+2. α2+β2=11.THIS WEEK's
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