If y = 3 x − 1 + 3 − x − 1 (x real), then the least value of y is Options: A . &nbsp2 B . &nbsp6 C . &nbsp23 D . &nbspNone of these

Answer: Option C : C We have 3 x − 1 + 3 − x − 1 = 1 3 ( 3 x + 3 − x ) ≥ 1 3 . 2 √ 3 x . 3 − x , [ ∵ A . M . ≥ G . M . ] or 3 x − 1 + 3 − x − 1 ≥ 2 3 Hence the least value of 3 x − 1 + 3 − x − 1 is 2 3

If y=3x−1+3−x−1 (x real), then the least value of y is

Question

y = 3^{x - 1} + 3^{- x - 1}

(x real), then the least value of y is

Options:

A . 2

B . 6

C . 23

D . None of these

Answer: Option C
:
C
We have

3^{x - 1} + 3^{- x - 1} = \frac{1}{3} (3^{x} + 3^{- x}) \geq \frac{1}{3} . 2 \sqrt{3^{x} . 3^{- x}}

[∵ A . M . \geq G . M .]

3^{x - 1} + 3^{- x - 1} \geq \frac{2}{3}

Hence the least value of

3^{x - 1} + 3^{- x - 1}

\frac{2}{3}

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. If a and b are two positive quantities whose sum is λ, then the minimum value of √(1+1a)(1+1b) is....

Question 2. If x=log53+log75+log97, then x ≥....

Question 3. If a, b, c be three real numbers of the same sign then the value of ab+bc+ca lies in the interval....

Question 4. If log4 5 = a and log5 6 = b, then log3 2 is equal to ....

Question 5. If the entry fee to a fair is $5 and each game at the fair costs $2 to play, write an inequality for the total cost when....and the maximum amount the person can spend is $25.

Question 6. Y≤3x+1x−y>1Which of the following ordered pairs (x,y) satisfies the system of inequalities above?....

Question 7. If 21bx−28>49, Where b is a positive constant, which of the following best describes all possible values of 4 ....following best describes all possible values of 4 - 3bx?

Question 8. If 3<p<7 and −9<q<−4, then what is the range of p - q?....

Question 9. Which of the following numbers is NOT a solution of the inequality 3x−5≥4x−3 ?....

Question 10. Log7 log7 √7(√7√7)=....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0

Submit Solution

More Questions on This Topic :

Latest Videos

Latest Test Papers