# how many solutions?

Discussion in 'Mathematics' started by coffee-breff, Mar 29, 2012.

1. ### coffee-breffNew commenter

I was doing some work with an very able year 10 class and set this for them
(x^2+5x+5)^(x^2+11x+30)=1
what are the solutions?

2. ### Polecat

How did they get on?

6

4. ### coffee-breffNew commenter

they found 4, some with algebra and some by graphing it. I have left them to find the others over Easter. They are convinced that there are no more.

5. ### ScifihelNew commenter

I get four solutions.

hang on...
just as well we can edit posts

thinking again, with pen and paper

6. ### KarvolOccasional commenter

Are you posing it as a question for the forum or are you posing it because you need to find out?
More importantly, what did your class learn from it?

7. ### ScifihelNew commenter

Formatting nightmare, with stupid keyboard.

8. ### KarvolOccasional commenter

-6, -5, -4 and -1 by observation. What others are there ( I need to go and cook dinner... )?

9. ### coffee-breffNew commenter

i think I know the answer, I just thought it was an interesting problem.

10. ### KarvolOccasional commenter

And -3 and -2 because the "base" can also be -1 if the "power" is even.

11. ### KarvolOccasional commenter

It looks like my Year 10 class have just got their first homework for after the holidays. Should make for some interesting class discussion...
Thanks!

12. ### jeff291

I would expect most half OK year 12/13s to do it. Year 10s? depends on their approach.....

13. ### wechselbalg

Are there not infinitely many? i.e. all the solutions that correspond to:
u^0 = 1
1^n=1
(-1)^(2n)=1
with some restrictions if you want real solns? (Nice question, BTW)

14. ### drnfp

Don't forget, u and n are not independent. If we force the exponent to be 0, then this fixes u.
By taking logs, I got the 6 solutions stated. Drawing a graph seems to confirm this.

15. ### wechselbalg

Yes, you're right. That'll teach me not to solve problems in my head, and to show all of my working.

16. ### drnfp

Looked at this with further maths today, we came to the conclusion that the theoretical max no. of solns is 10. 2 from the power and 8 from putting base = 1, -1, i, -i provided the power then met certain criteria. Do you agree?

17. ### logicmaths

What were your solutions for x when the base was i, and -i?