## anonymous 4 years ago How do I get from 2a+a+sqrt(3a^2)=20 to.... a=8.453?

1. anonymous

How did you arrive at that answer?

2. anonymous

wolframalpha.com

3. anonymous

are you sure you plugged it in correctly?

4. anonymous

I entered the equation exactly how it here.

5. anonymous

Then you must've typed it here wrong. That is not the correct answer.

6. anonymous

Double check

7. anonymous

http://www.wolframalpha.com/input/?i=2a%2Ba%2B+sqrt%283a%5E2%29%3D20 are you able to see this, my friend?

8. anonymous

$2a+a+\sqrt(3a^2)=20$

9. anonymous

Yes, that correct.

10. anonymous

It doesn't say the answer is 8.453

11. anonymous

It does, in the solution: a=-10/3(sqrt(3)-3).

12. anonymous

That comes out to approximately 4.2265

13. anonymous

Not 8.453

14. anonymous

You're right I made a mistake, my answer is two times 4.2265.

15. anonymous

OK i will show you how to do the work correctly.

16. anonymous

I am still wondering how I get there though.

17. anonymous

$3a+\sqrt(3a^2)=20$ $a(3+\sqrt(3))=20$ $a=\frac{20}{(3+\sqrt(3))}$

18. anonymous

From here we rationalize the denominator

19. anonymous

I am confused in the second step.

20. anonymous

$\frac{20}{3+\sqrt(3)} * \frac{3-\sqrt(3)}{3-\sqrt(3)}$

21. anonymous

In the second step i simply factored out an a because $\sqrt(a^2)=a$

22. anonymous

so it would be $3a+a \sqrt(3)$

23. anonymous

Then you can factor out an a here, see?

24. anonymous

okay, i see now thank you very much !

25. anonymous

Do you know how to rationalize the denominator?

26. anonymous

You must do that to get to the final answer

27. anonymous

I do, i need to try it to make sure i get the mechanics of it.

28. anonymous

The numberator should be 60-20sqrt(3), correct? And I am having difficulties with the denominator? Could you help please?

29. anonymous

Nevermind, I figured it out, thank you.