ytrewqmiswi one year ago solutions

1. ytrewqmiswi

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

2. welshfella

by inspection one value is 0.

3. ytrewqmiswi

yes :)

4. welshfella

oh so is 1 agreed?

5. ytrewqmiswi

yes

6. welshfella

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

7. welshfella

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

8. ytrewqmiswi

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

9. welshfella

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

10. welshfella

I'll check it out

11. ytrewqmiswi

ok

12. welshfella

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

13. welshfella

-5 is an extraneous solution

14. ytrewqmiswi

yes