Question

Find the value of x satisfying the equations

5{x} = x + [x] and [x] – {x} =

1

2​

Answer 1

Answer:

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Answer 2

Answer:

Given equation is: 5

2x

−5

x+3

+125=5

x

Let 5

x

=t

Hence, t

2

−5

3

.t+125=t

⇒t

2

−126t+125=0

⇒t

2

−126t−t+125=0

⇒t(t−125)−1(t−125)=0

⇒(t−1)(t−125)=0

⇒t=1 and t=125

Hence, 5

x

=1=5

0

or 5

x

=125=5

3

Therefore, x=0 or x=3