Question

x + y = 10, x^2 + y^2 = 58 then x^3 + y^3 = ?

Answer 1

Hello student,
Please find the answer to your question below
a³ + b³ = (a + b) (a² - ab + b²)
= 10 (58 - ab)
But (a + b)² = a² + 2ab + b² = 58+2ab
also (a+b)^2=10² = 100 since a+b=10
58+2ab=100
=> 2ab =100-58=42
=> ab = 21
=>a³ + b³ = (a + b) (a² - ab + b²)
= 10 (58 - ab)
=10*(58 - 21) = 370