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.