Question 86

If the product of n positive real numbers is unity, then their sum is necessarily

Name: If the product of n positive real numbers is unity, then their sum is necessarily
Uploaded: Oct. 7, 2024, 4:50 p.m.
Duration: 1 min 4 s
Description: If the product of n positive real numbers is unity, then their sum is necessarily

Solution

Let the numbers be $$a_1,a_2....a_n.$$

Since the numbers are positive,

$$AM\geq GM$$

$$\frac{a_1+a_2+a_3....+a_n}{n}\geq (a_1*a_2....*a_n)^{1/n}$$

$$a_1+a_2+a_3....+a_n \geq n$$

Share on Whatsapp Share on Whatsapp

Boost your CAT prep: Take All-India 3 free CAT mock tests with Video solutions

Video Solution

Click on the Email ☝️ to Watch the Video Solution

Create a FREE account and get:

All Quant CAT complete Formulas and shortcuts PDF
38+ CAT previous year papers with video solutions PDF
5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Linear Equations Questions CAT Logarithms, Surds and Indices Questions CAT Coordinate Geometry Questions CAT Arithmetic Questions CAT Inequalities Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Arrangement Questions CAT Data Interpretation Basics Questions CAT Venn Diagrams Questions CAT Data Interpretation Questions CAT Coins and Weights Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Para Jumbles Questions CAT Odd One Out Questions CAT Verbal Ability Questions CAT Reading Comprehension Questions CAT Miscellaneous Questions

Also Read

CAT Mock Tests

CAT 2025 Course

Free CAT Preparation

CAT Questions

CAT Formulas PDF

CAT Study Material

CAT Score vs Percentile

CAT Score Calculator

CAT Percentile Predictor

CAT Sectional Tests

CAT Exam

CAT Prep Videos

CAT Registration

CAT Syllabus 2025

CAT Eligibility Criteria

CAT Admit Card

CAT 2003 QA (Leaked) Question

If the product of n positive real numbers is unity, then their sum is necessarily

Video Solution

CAT Quant Questions | CAT Quantitative Ability

CAT DILR Questions | LRDI Questions For CAT

CAT Verbal Ability Questions | VARC Questions For CAT

Also Read

Free CAT Quant Questions

Login to your Cracku account

Hello! 👋

Ready to Unlock Your Success?

Please Enter Your OTP

Please enter the following details

Create a free Cracku account

Get Started with 5000+ Free CAT Questions & Mock Tests with Detailed Solutions!