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Find all possible values of (x^2+1)/(x^2...

Find all possible values of `(x^2+1)/(x^2-2)` .

Text Solution

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`(x^2+1)/(x^2-2)`
or `yx^2-2y= x^2+1`
or `x^2=(2y+1)/(y-1)`
Now `x^2 ge 0 rArr (2y+1)/(y-1) ge 0`
Now `x^2 ge 0 rArr (2y +1)(y-1) le 0`
`rArr y le -1//2 or y gt 1`
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