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$If x \in R, the numbers (5^{1 + x} + 5^{1 - x}), \frac{a}{2}, (25^{x} + 25^{- x}) from an A.P then 'a' must lie in the imterval :$

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Correct option is D

a=51+x+51−x+25x+25−xa=55x+15x+5x+15x2−2 Let t=5x+15xa=5t+t2−2a=t2+5t−2;t≥2a≥4+10−2a≥12

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If x∈R, the numbers 51+x+51−x,a2,25x+25−x from an A.P then 'a' must lie in the imterval :

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$If x \in R, the numbers (5^{1 + x} + 5^{1 - x}), \frac{a}{2}, (25^{x} + 25^{- x}) from an A.P then 'a' must lie in the imterval :$