Question

solutions

Answer 1

\[[x^2]+[2x]=3x\]
[]=greatest integer function\[x \in [0,2]\]
find the values of x

Answer 2

by inspection one value is 0.

Answer 3

yes :)

Answer 4

oh so is 1 agreed?

Answer 5

yes

Answer 6

If we square both sides we get
x^4 + 4x^3 + 4x^2 = 9x^2

Answer 7

x^4 + 4x^3 - 5x^2 = 0
x^2(x^2 + 4x - 5) = 0
x^2(x + 5)(x - 1) = 0

x = 0, 1 , -5

Answer 8

but is it ok to square nd simplify like that when u have greatest integer function there?

Answer 9

to be honest i'm not sure
1 would be greatest integer function i guess

Answer 10

I'll check it out

Answer 11

ok

Answer 12

[0,2] must be the domain so the greatest integer function would be 1

Answer 13

-5 is an extraneous solution

Answer 14

yes