If x € R, the numbers 51+x + 51-x, ...
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If x € R, the numbers 51+x + 51-x, a/2, 25x + 25-x form an A.P. then 'a' must lie in the interval: (A) [1, 5] (B) [2, 5] (C) (5, 12] (D) [12,)

JEE/Engineering Exams
Maths
Solution
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( left(5^{12 x}+5^{1-x}right)+left(25^{x}+25 xright)=2left(frac{9}{2}right) ) ( sin left(5^{x}+frac{1}{5}right)+left(45^{x}+frac{1}{25^{x}}right)=a rightarrow ) Ear ( x=0, a=12 ) Pon ( x>0 ) is a valur kevps on increating ( operatorname{Dax} x theta ) notice in 0 'a' ralue frougs on increasing ( r ) )
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