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If a + (1)/(a -2)=4, then the value of (...

If `a + (1)/(a -2)=4,` then the value of `(a -2) ^(2) + ((1)/(a -2)) ^(2)` is:

A

0

B

2

C

-2

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
`a+(1)/(a-2)=4`
`a-2 +(1)/(a-2)=2`
`(a-2)^(2)+{(1)/((a-2))}^(2)=((a-2)+(1)/((a-2)))^(2)-2`
`=(2)^(2)-2`
`=4-2 =2`
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