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If the range of function f(x)=((pi)/(sqr...

If the range of function `f(x)=((pi)/(sqrt(2))+sin^(-1)alpha)x^(2)+2(sin^(-1)beta)x+(pi)/(sqrt(2))-sin^(-1)alpha` is `[0,oo)` ,then the maximum value of `(a^(2)+beta^(2)+a^(2)beta^(2))` is equal to

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