Question

The number of solutions of the
equation x+ +[x] – 4x +3=0 is Where []
denotes G.I.F.​

Answer 1

Answer:

x^2−4x+[x]=0

Now   ^2

+4x=(−[x])

(1) When xϵ[0,1)⇒[x]=0

x^2−4x=0⇒x=0,4 but we have assumed

xϵ[0,1)

So only   ′  0  ′  is solution

(2) When xϵ[1,2)⇒[x]=1

4x^2−4x=−1⇒x=$(2+\sqrt{3} ),(2-\sqrt{3} )$

Both are not in assumed range so rejected

(3) When x=2⇒[x]=2

x^2−4x=−2⇒x=$(2+\sqrt{2} ),(2-\sqrt{2} )$

∴x  ^2  =4x+[x]=0 has only one solution

ln[0,2] i.e.   ′  0  ′ .