1. ## Clculate a^2+b^2

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

2. Originally Posted by dhiab
If : $\displaystyle (a^{3}=3ab^{2}+11)and(b^{3}=3a^{2}b+2)$
Calculate : $\displaystyle a^{2}+b^{2}$
a, b in R.( no calculate a,b).
hmm..

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

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

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

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

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

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

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

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

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

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

6. <essafty>

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