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Question
`a = 1/(a - 2). ∴ a - 1/a=` ______.
Options
4
3
2
1
MCQ
Fill in the Blanks
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Solution
`a = 1/(a - 2). ∴ a - 1/a =` 2.
Explanation:
a(a − 2) = 1
a2 − 2a − 1 = 0
Using the quadratic formula:
`a = (-(-2) + -sqrt((-2)^2 - 4(1) (-1)))/(2(1))`
`a = (2 + -sqrt(4 + 4))/2`
`a = (2 + -sqrt8)/2`
`a = (2 + -2sqrt2)/2`
`a = 1 + -sqrt2`
Finding, `a - 1/a`
`a - 1/a = (1 + sqrt2) - (-1 + sqrt2)`
`a - 1/a = 1 + sqrt2 + 1 - sqrt2`
`a - 1/a = 1 + 1`
`a - 1/a = 2`
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