{x+1}+2x=4[x+1]-6

Discussion Response Post to: {x+1}+2x=4[x+1]-6

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as we know...{x}=x-[x]

(x+1)-[x+1]+2x=4[x+1]-6

3x+1=5[x+1]-6

3x+1=5([x]+1)-6

3([x]+{x})=5[x]-2

3{x}=2[x]-2................(1)

as we know..0<={x}<1

0<=3{x}<3........................(2)

on substitutin...(1)

we get..

1<=[x]<5/2...so we conclude that...[x]=1 or 2.

hence from (1)..3{x}=2*1-2=0

or {x}=0 or 2/3.

x={x}+[x]...1+0 or 2+2/3 i.e

1,8/3 are solutions.....

nudge me if i m wrong....

B Tech- IIIrd year Dep:- MEMS IIT Bombay Hostel-9

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