a3+b3 = 600, a + b = 10. Найдите ab.

a³ + b³ = 600;

a³ + b³ = (a + b) (a² - ab + b²);

a + b = 10;

(a + b) ² = 102;

a² + 2ab + b² = 100;

a² + b² = 100 - 2ab

a³ + b³ = 10 (a² - ab + b²);

a³ + b³ = 10 (100 - 2ab - ab);

a³ + b³ = 1000 - 30ab;

1000 - 30ab = 600;

-30ab = 600 - 1000;

-30ab = - 400;

ab = 400/30;

ab = 40/3.