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Solve : (log)(0. 3)(x^2-x+1)>0...

Solve : `(log)_(0. 3)(x^2-x+1)>0`

Text Solution

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`log_(0.3)(x^(2)-x+1) gt 0 or 0 lt x^(2)-x+1 lt (0.3)^(0)`
` or 0 lt x^(2)-x+1 lt 1`
` rArr x^(2)-x+1 gt 0 and x^(2) - x lt 0`
` or x (x-1) lt 0`
` rArr 0 lt x lt 1 ("as " x^(2)-x+1=(x-1//2)^(2)+3//4 gt 0," for all real x")`
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