If a(a>0) is the value of parameter for each of which the are of the figure bounded by the straight line y=1+a4a2−ax and the parabola y=1+a4x2+2ax+3a2 is the greatest, then the value of a4 is ___

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Question

If $a (a > 0)$ is the value of parameter for each of which the are of the figure bounded by the straight line $y = \frac{a ^{2} - a x}{1 + a ^{4}}$ and the parabola $y = \frac{x ^{2} + 2 a x + 3 a ^{2}}{1 + a ^{4}}$ is the greatest, then the value of $a^{4}$ is ___

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a (a > 0)

is the value of parameter for each of which the are of the figure bounded by the straight line

y = \frac{a ^{2} - a x}{1 + a ^{4}}

and the parabola

y = \frac{x ^{2} + 2 a x + 3 a ^{2}}{1 + a ^{4}}

is the greatest, then the value of

a^{4}

is ___

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Question Text

a (a > 0)

is the value of parameter for each of which the are of the figure bounded by the straight line

y = \frac{a ^{2} - a x}{1 + a ^{4}}

and the parabola

y = \frac{x ^{2} + 2 a x + 3 a ^{2}}{1 + a ^{4}}

is the greatest, then the value of

a^{4}

is ___