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  1. If   a +
    1
    		 = 4, then the value
    of (a − 2)2 +
    1
    		2 is :
    a − 2a − 2
    1. 0
    2. 2
    3. –2
    4. 4
Correct Option: B

a +
1
 = 4
a − 2

⇒  (a − 2) +
1
 = 4 − 2 = 2
(a − 2)

On squaring both sides,
(a − 2) +
1
2 = 4
(a − 2)

⇒  (a − 2)2 +
1
 + 2 × (a − 2) ×
1
 = 4
(a − 2)2(a − 2)

⇒  (a − 2)2 +
1
 = 4 − 2 = 2
(a − 2)2


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