Question

if x+y = a and x2+y2 = b then find the value of x3+y3

Answer 1

I hope it will help you mate

Answer 2

Answer:

Step-by-step explanation

x +y = a

square on both sides

you will get

x² + y² + 2xy = a²

b + 2xy = a²

2xy = a² - b

xy = a² -b /2

cube the same equation and you will get

(x+y)³ = a³

x³ + y³ + 3xy (x+y) = a³

x³ +y³ + 3 (a² -b /2) (a ) = a³

x³ +y³ + 3 ( a³ - ab /2) = a³

x³+y³ + (3a³ - 3ab) /2 = a³

multiply the whole equation by 2

2x³ +2y³ +3a³ - 3ab = 2a³

2(x³ + y³) = 2a³ - 3a³ + 3ab

2(x³ +y³) = 3ab - a³

x³ + y³ = 3ab-a³  /2