Clculate a^2+b^2

**dhiab** · June 4th 2010, 06:03 PM

If : $(a^{3}=3ab^{2}+11)and(b^{3}=3a^{2}b+2)$
Calculate : $a^{2}+b^{2}$
a, b in R.( no calculate a,b).

**AllanCuz** · June 4th 2010, 06:34 PM

Originally Posted by dhiab

If : $(a^{3}=3ab^{2}+11)and(b^{3}=3a^{2}b+2)$
Calculate : $a^{2}+b^{2}$
a, b in R.( no calculate a,b).

hmm..

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

$a^3 + b^3 = 3ab^2 + 11 + 3a^2 b + 2$

$a^2 - ab +b^2 = \frac{ 3(ab^2 + a^2b) +13 }{ a+b }$

$a^2 + b^2 = \frac{ 3(ab^2 + a^2b) +13 }{ a+b } + ab$

$a^2 + b^2 = \frac{ 3(ab^2 + a^2b) +13 + a^2b + b^2a}{ a+b }$

$a^2 + b^2 = \frac{ 4(ab^2 + a^2b) +13 }{ a+b }$

Does the question want the above in terms of a value (i.e. right side cant have a or b in it)?

**essafty** · June 19th 2010, 01:37 PM

Originally Posted by dhiab

If : $(a^{3}=3ab^{2}+11)and(b^{3}=3a^{2}b+2)$
Calculate : $a^{2}+b^{2}$
a, b in R.( no calculate a,b).

**arpitagarwal82** · June 19th 2010, 03:01 PM

Very smart solution essafty.
Where is the thanks button gone??

**Bacterius** · June 19th 2010, 05:12 PM

Nicely done, Essafty ! Well presented, too. If there was a thanks button I'd be hitting it

**pacman** · June 23rd 2010, 06:12 PM

<essafty>

what a clever solution you have shown . . . . i like it

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