Solve for a
a\in \left(0,1\right)
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a-a^{2}>0
Subtract a^{2} from both sides.
-a+a^{2}<0
Multiply the inequality by -1 to make the coefficient of the highest power in a-a^{2} positive. Since -1 is negative, the inequality direction is changed.
a\left(a-1\right)<0
Factor out a.
a>0 a-1<0
For the product to be negative, a and a-1 have to be of the opposite signs. Consider the case when a is positive and a-1 is negative.
a\in \left(0,1\right)
The solution satisfying both inequalities is a\in \left(0,1\right).
a-1>0 a<0
Consider the case when a-1 is positive and a is negative.
a\in \emptyset
This is false for any a.
a\in \left(0,1\right)
The final solution is the union of the obtained solutions.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Matrix
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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