Question

Відомо, що а + b = 6, ab = 16. Знайти а3 + b3.
Поясніть бо не розумію

Answer 1

$\displaystyle\bf\\ab=16\\\\a+b=6\\\\(a+b)^{2} =6^{2} \\\\a^{2} +2\cdot \underbrace{ab}_{16}+b^{2} =36\\\\a^{2}+32+b^{2} =36\\\\\boxed{a^{2} +b^{2} =4}\\\\\\a^{3} +b^{3} =(a+b)\cdot(a^{2} -ab+b^{2})= (\underbrace{a+b}_{6})\cdot(\underbrace{a^{2} +b^{2}}_{4}-\underbrace{ab}_{16})= \\\\\\=6\cdot(4-16)=6\cdot(-12)=-72$