## Problem Of The Week 43

**Find the number of real roots (x+1)^x=x^(x+1)**

Advertisements

For All Your Quant Queries

Written by Implex

October 4, 2008 at 2:10 am

Posted in Algebra, Problem of the week

Tagged with Algebra, Problem of the week

Subscribe to comments with RSS.

- Para Jumbles 19.08.09
- Fill In the blanks 08.08.09
- Fill In The Blanks 05.08.09
- Para Jumbles 05.08.09
- Para Jumbles 04.08.09

- Algebra
- Announcements
- Arithmetic
- CAT 2008
- CAT 2009
- Combinatorics
- concepts
- Conundrum
- Coordinate Geometry
- Data Sufficiency
- Functions
- General
- Geometry
- IIM Interview Experiences
- Inequalities
- Mock Cat
- Mock Quant
- Number Thoery
- Online CAT
- Power Play
- Prime Numbers
- Probability
- Problem of the week
- Problems
- Tips

- Problem of the day 26.08.09
- Problem of The day 06.08.09
- Problem of the Day 30.07.09
- Bonus QUestion 28.07.09
- Problem of the day 28.07.09

- Art of Problem Solving
- CAT Material (free)
- Math Lessons
- Pagal Guy
- Pagalbille
- Test Funda
- Verbal Logic

sujeet3035 on Problem of the day 17.07.… | |

vinit on Bonus Question 26.07.09 | |

harsh bansal on The Funny Side of Mathema… | |

KT on IIM A Interview Experienc… | |

tushar on Concept 3 Circle and Triangles… |

- 126,959 hits

- RT @akhileshsharma1: कुछ पत्रकारों के जबर्दस्त सेवा करने के बावजूद उन्हें राज्य सभा न भेज कर आम आदमी पार्टी ने 'तंगदिली' दिखाई। जबकि 'दरिया… 5 days ago
- RT @HectorBellerin: Looks like you couldn't see today either @T_Deeney 😂 twitter.com/btsportfootbal… 6 days ago
- RT @arseblog: YES HECTOR! twitter.com/HectorBellerin… 6 days ago
- RT @theskindoctor13: Syphilis has heart complications like aortitis, regurgitation, heart failure. Heart failure is end result of many dise… 1 week ago
- RT @coolfunnytshirt: tum saala gutter chhaap badboodaar hindustani keede makode log, tumhari aukat kya thi Nehru ke khaandaan ke raaj se pa… 1 week ago

Advertisements

%d bloggers like this:

No solution!But I couldn’t find any method do prove it..

Celebrating LifeOctober 4, 2008 at 3:34 am

try again !!

outtimedOctober 4, 2008 at 5:02 am

One solution

-1

tyroOctober 4, 2008 at 5:45 am

what is the method?

outtimedOctober 4, 2008 at 6:12 am

I took log to the base x of both sides and solved it for x.

tyroOctober 4, 2008 at 6:19 am

But then x can’t be -1. so it could be no solution.

tyroOctober 4, 2008 at 7:14 am

there is a solution try again !

outtimedOctober 4, 2008 at 7:23 am

I tried constructing a graph for the equation. Infinite real roots?

Totally confused with the question. @ Outtimed can you please explain the answer.

riyaOctober 4, 2008 at 10:40 am

The graph is a straight line parallel to an axis

tyroOctober 4, 2008 at 11:49 am

The value of x or if we think of it as values , will lie between 2 and 3 as for 2 or less than 2 one side of the equation becomes greater than the other and for 3 or greater than 3 , the other side of the equation becomes greater.

tyroOctober 4, 2008 at 12:46 pm

x comes to be the xth root of (1+1/x). Thus this forms an infinite series.

tyroOctober 4, 2008 at 2:24 pm

log(x+1)/(x+1)=logx/x

take f(y)=logy/y

plot the graph

now check if you can find a solution or not

hint: the graph does not rise or dip monotonously!

outtimedOctober 4, 2008 at 4:24 pm

basically we get

(1+1/n)^n =n

so basically we get one root between 2 and 3 and later on as limit of left hand side is e when n approaches infinity.. so just one root..

VarunOctober 4, 2008 at 6:05 pm

plotting the graph for log y/y between y=2 to 4 we get a curve which first increases then decreases, the value is almost same for 2.3 and 3.3, around 0.157

tyroOctober 5, 2008 at 3:53 am