Question

The number of non zero solutions of the equation 3[x] = 5{x} + x; where [·] and {·} denotes the greatest integer function and fractional function respectively, is


Zero


One


Two


Three

Answer 1

Answer:

2

Step-by-step explanation:

[·] and {·} denotes the greatest integer function and fractional function respectively.

So we can write x = [x] + {x}

Now coming to the question,

3[x] = 5{x} + x

⇒ 3[x] = 5{x} + [x] + {x}

⇒ 3[x] - [x] = 5{x} + {x}

⇒ 2[x] = 6{x}

⇒ [x] = 3{x}

⇒ {x} = [x] / 3

Since [x] is the integral part,

if [x] = 1, {x} = 1/3 = 0.333; x = 1 + 0.333 = 1.333

if [x] = 2, {x} = 2/3 = 0.667 ;  x = 2 + 0.667 = 2.667

if [x] = 3, {x} = 3/3 = 1, (discarded as {x} is always less than 1)

So there are 2 non-zero solutions: x = 1.333 and 2.667

Answer 2

Step-by-step explanation:

[-] and [-] denotes the greatest integer function

and fractional function respectively.

So we can write x = [x] + {x}

Now coming to the question,

3[x]=5[x]+x

⇒ 3[x] = 5{x} + [x] + {x}

⇒ 3[x]-[x] = 5{x} + {x}

⇒ 2[x] = 6[x]

⇒ [x] =3[x]

⇒ [x] = [x]/3

Since [x] is the integral part,

if [x]=1,[x]=1/3=0.333 x = 1+ 0.333 = 1.333

if [x]=2,[x]=2/3=0.667 ; x = 2 + 0.667 = 2.667

if [x] = 3, [x] = 3/3 = 1, (discarded as {x} is always

less than 1)

So there are 2 non-zero solutions: x=1.333

and 2.667