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Let alpha1 and alpha2 be two real value...

Let `alpha_1 and alpha_2` be two real values of `alpha` for which the numbers `2alpha^2,alpha^4,24` taken in that order form an arithmetic progression, If `beta_1 and beta_2` are two real values of `beta` for which the number `1,beta^2,6-beta^2` taken in the order form a geometric progression, then find the value of `(alpha_1^2+alpha_2^2+beta_1^2+beta_2^2).`

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