TeemoTheTerific 2 years ago Hi... Last question and i can sleep peacefully :) THANKS

1. TeemoTheTerific

$\huge a= 2^{\frac{ 1 }{ 2 }} + 2^{\frac{ -1 }{ 2 }}$ $\huge b=2^{\frac{ 1 }{ 2 }} - 2^{\frac{ -1 }{ 2 }}$ FIND $\huge a ^{3} + b ^{3}$

2. TeemoTheTerific

lol someone randomly gave me a medal?

3. TeemoTheTerific

i know the formula for a^3 + b^3 btw

4. TeemoTheTerific

(a+b)(a^2-ab + b^2)

5. hartnn

so, a+b=.. ?

6. hartnn

its actually $$2 \times 2^{1/2}$$

7. TeemoTheTerific

yea :)

8. hartnn

ok, keep that as it is... now try (a^2-ab + b^2) =... ?

9. TeemoTheTerific

same thing as 2^1/2 + 2^1/2

10. TeemoTheTerific

i worked out a^2 was 9/2 before

11. hartnn

9/2 ? just a second..

12. TeemoTheTerific

b^2 was also ummm 1/2

13. hartnn

$$(a^2-ab+b^2 )= (a^2-2ab+b^2)+ab = (a+b)^2+ab$$ you already know a+b

14. hartnn

find ab

15. hartnn

we know a+b = 2*2^(1/2)

16. TeemoTheTerific

ab = 3/2?

17. hartnn

yes :)

18. TeemoTheTerific

would it be (a-b)^2 + ab? instead of (a+b)^2 + ab

19. hartnn

sorry, my mistake

20. hartnn

$$(a^2-ab+b^2 )= (a^2+2ab+b^2)-3ab = (a+b)^2-3ab$$

21. TeemoTheTerific

so ill just work out (a^2-ab + b^2) manually?

22. TeemoTheTerific

wait but i dont think i done (a+b)^2

23. hartnn

i was just trying to simplify...you can do that manually, but it'll become complicated...

24. TeemoTheTerific

(a+b)^2 would be 8?

25. hartnn

yes. ab = 3/2 so, -3ab = -9/2 and 8+9/2 =... ?

26. hartnn

*8-9/2=..

27. TeemoTheTerific

7/2

28. TeemoTheTerific

so answer is (2^1/2 times 2 )(7/2) Is it?

29. hartnn

$$2 \times 2^{(1/2)} \times 7/2 =2^{(1/2)} \times 7$$

30. TeemoTheTerific

ok thank you so much

31. TeemoTheTerific

these question confuse me so much :(

32. hartnn

practice more.... all confusions will go away...

33. TeemoTheTerific

lol thats easy to say