Home
Class 12
MATHS
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)`
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|5 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Linked comprehension type|6 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Concept Application Eexercises 6.4|4 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

  • INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|762 Videos

Similar Questions

Explore conceptually related problems

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

If (x+y,y-2) = (3,1), find the values of x and y.

If (x+1, y-2)=(3,1), find the values of x and y.

If y = 3e^(2x)+2e^(3x) then show that y_2-5y_1 +6y=0

If x=1+3^(2/3)+3^(1/3) , find the value of (x^3-3x^2-6x-4) .

If (x+3+1, y-2/3)=(5/3, 1/3) , find the values of x and y.

If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y) is 1 (b) (log)_2 3- (log)_3 2 (c) log(3/2) (d) none of these

If {:[(2x-y,5),(3,y)]={:[(6,5),(3,-2)] , then the value of x is____

CENGAGE PUBLICATION-INEQUALITIES INVOLVING MEANS -EXERCISES (Single Correct answer type)
  1. The minimum value of (x^(4)+y^(4)+z^(2))/(xyz) for positive real numbe...

    Text Solution

    |

  2. A rod of fixed length k slides along the coordinates axes, If it meets...

    Text Solution

    |

  3. The least value of 6tan^2varphi+54cot^2varphi+18 is 54 when A.M.geq GM...

    Text Solution

    |

  4. If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the mi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is a. 3...

    Text Solution

    |

  9. If l ,m ,n are the three positive roots of the equation x^3-a x^2+b x-...

    Text Solution

    |

  10. If positive numbers a ,b ,c are in H.P., then equation x^2-k x+2b^(101...

    Text Solution

    |

  11. For x^2-(a+3)|x|-4=0 to have real solutions, the range of a is a)(-oo...

    Text Solution

    |

  12. If a ,b ,c are the sides of a triangle, then the minimum value of a/(b...

    Text Solution

    |

  13. If a,b,c,d in R^(+)-{1}, then the minimum value of log(d) a+ log(c)b+l...

    Text Solution

    |

  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...

    Text Solution

    |

  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...

    Text Solution

    |

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

    Text Solution

    |

  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+...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |