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Find the complete set of values of a suc...

Find the complete set of values of a such that `(x^2-x)//(1-a x)` attains all real values.

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The correct Answer is:
` ain [1, infty)` ,
`y= (x^(2) - x)/ (1 - ax)`
or `x^(2) - x = y - axy`
or ` x^(2) + x (ay - 1) - y = 0`
Since x is real, so
`(ay - 1)^(2) + 4y ge 0`
`rArr a^(2) y^(2) + 2y (2-a) + 1 ge 0, AA y in ` R
`rArr a^(2) gt 0, 4(2 - a)^(2) - 4a^(2) le 0 rArr 4 - 4a le 0 rArr a in [ 1 , infty)` .
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