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If ' a^(prime)(a >0) is the value of par...

If `' a^(prime)(a >0)` is the value of parameter for each of which the area of the figure bounded by the straight line `y=(a^2-a x)/(1+a^4)` and the parabola `y=(x^2+2a x+3a^2)/(1+a^4)` is the greatest, then the value of `a^4` is___

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