equations

Q1 solve for x:

[lnex]( x2011 + 2011x - 2011) - [lne(1/x)]2011 = 0

9 Answers

62
Lokesh Verma ·

is that greatest integer? or just a simple bracket?

11
vaibhav sharma ·

no greatest integer all brackets are simple brackets

62
Lokesh Verma ·

\\k^{(x^{2011}+2011x-2011)}=k^{-2011} \\(x^{2011}+2011x-2011)=-2011 \\x^{2011}+2011x=0 \\

another case will be when k=0 or 1

so x=1, x=e,

11
vaibhav sharma ·

but sir

it is [-k]2011 not [k]-2011

62
Lokesh Verma ·

oops i wrote it wrongly.. i was thinking the right thing but :(

1
ARKA(REEK) ·

-[-k]2011 should be equal to +[k2011] .... since power is odd ...

11
vaibhav sharma ·

sir x=1 a solution ..gotta find other solutions too

@arka
i don't think using -[-k]2011 = [k]2011 wud help here
if we use this we wud get

[k]m = -[k]2011 , m = x2011 + 2011x - 2011

now again we can't compare the powers

1
ARKA(REEK) ·

@Vaibhav

Arre yaar ... I didn't mean that .... From Nishant bhaiyya's logic ... I just said that [lne(1/x)]2011 can be written as [-lnex]2011 = [-k]2011 ... Now since there is a (-) before the expr. ... we can simplify [-k]2011 into -[k2011] .. since 2011 is odd ... and make the ultimate expr. +[k2011] ...

1
ARKA(REEK) ·

@ Vaibhav ... Sorry .. I figured it out wrong ... u were right !!!

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