if $a+ b = 9 $and $ab = 1$. what will be the $a^3 + b^3 =$?

Question

How can I solve this? Or, is it given properly? If $a + b = 9$ and $ab = 1$. What is $a^3 + b^3 = $?

@TonyK thank you :) thats more easier. Yet I'm growing. – Rufat Nuriev Dec 02 '14 at 20:17 — Rufat Nuriev, Dec 02 '14 at 20:17

score 4 · Answer 1 · answered Dec 02 '14 at 19:59

4

You can start with the fact that $$a^3+b^3=(a+b)(a^2-ab+b^2) $$ $$(a+b)^2 = a^2+2ab+b^2$$ And see if you can use some substitutions, additions and subtractions.

answered Dec 02 '14 at 19:59

turkeyhundt

7,733

The LHS of your first equation should be $a^3 + b^3$ – RHP Dec 02 '14 at 20:01
whoops. thanks. – turkeyhundt Dec 02 '14 at 20:02

score 2 · Answer 2 · answered Dec 02 '14 at 19:59

2

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

answered Dec 02 '14 at 19:59

DeepSea

77,651

That's somewhat more than a hint.... – Dec 02 '14 at 20:04

score 0 · Answer 3 · answered Dec 02 '14 at 20:01

0

Hint: Express $a^3+b^3$ as function of $ab$ and $a+b$.

answered Dec 02 '14 at 20:01

Leox

8,120

score 0 · Accepted Answer · answered Dec 02 '14 at 20:01

0

$a + b = 9 => a = 9 - b$ and then you solve $b$: $ab = 1 => (9 - b)b = 1$; solving $a$ is easy now. (then $a^3 + b^3 = ...$ is easier)

answered Dec 02 '14 at 20:01

LyingOnTheSky

58

2

@Rufat, why did you choose the least helpful answer to accept? – TonyK Dec 02 '14 at 20:15
@TonyK Just I understand them, the second one was more easier than the first one. Thank you! – Rufat Nuriev Dec 03 '14 at 15:25

score 0 · Answer 5 · answered Jan 01 '15 at 07:31

0

$$a^2+b^2=(a+b)^2-2ab$$ $$a^3+b^3=(a+b)^3-3ab(a+b)$$ $$a^4+b^4=(a+b)^4-4ab(a+b)^2+2a^2b^2$$ $$a^5+b^5=(a+b)^5-5ab(a+b)^3+5a^2b^2(a+b)$$

answered Jan 01 '15 at 07:31

Bumblebee

18,220
5
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if $a+ b = 9 $and $ab = 1$. what will be the $a^3 + b^3 =$?

5 Answers5