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If y=3^(x-1)+3^(-x-1) , then the least v...

If `y=3^(x-1)+3^(-x-1)` , then the least value of `y` is `2` `6` `2//3` `3//2`

A

2

B

6

C

`2//3`

D

`3//2`

Text Solution

Verified by Experts

The correct Answer is:
C
`y = (3^(x))/(3) + (1)/(3^(x) 3)`
Now,
`A.M ge G.M`
`implies ((3^(x))/(3) + (1)/(3^(3^(x) 3)))^(2) ge sqrt((3^(x))/(3) (1)/(3^(x) 3))`
Or `3^(x - 1) + 3^(-x - 1) ge (2)/(3)`
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CENGAGE ENGLISH-INEQUALITIES INVOLVING MEANS -EXERCISES (Single Correct answer type)
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  5. If y=3^(x-1)+3^(-x-1) , then the least value of y is 2 6 2//3 3//2

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  6. Minimum value of (b+c)//a+(c+a)//b+(a+b)//c (for real positive numbers...

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  7. If the product of n positive numbers is n^n , then their sum is a posi...

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  14. If a ,b ,c in R^+, t h e n(b c)/(b+c)+(a c)/(a+c)+(a b)/(a+b) is alwa...

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  15. If a ,b ,c in R^+t h e n(a+b+c)(1/a+1/b+1/c) is always geq12 geq9 lt...

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  16. If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c...

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  17. If a ,b ,c ,d in R^+a n da ,b ,c are in H.P., then a+d > b+c a+b > c+...

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  18. If a ,b ,c ,d in R^+ such that a+b+c=18 , then the maximum value of a...

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  19. f(x)=((x-2)(x-1))/(x-3), forall xgt3. The minimum value of f(x) is equ...

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  20. If a >0, then least value of (a^3+a^2+a+1)^2 is (a)64 a^2 (b)16 a^4 ...

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