If x+y=a and x^2+y^2=b then find the value of x^3+y^3
Answers
Answered by
5
(x+y)²=x²+y²+2xy
=> a²=b+2xy
=> xy=(a²-b)/2
(x+y)³=x³+y³+3xy(x+y)
=> a³=x³+y³+(3/2)(a²-b)(a)
=>x³+y³=a³-(3/2)(a³-ab)
=>x³+y³=[2a³-3a³+3ab]/2
=> x³+y³=[3ab-a³]/2
=> a²=b+2xy
=> xy=(a²-b)/2
(x+y)³=x³+y³+3xy(x+y)
=> a³=x³+y³+(3/2)(a²-b)(a)
=>x³+y³=a³-(3/2)(a³-ab)
=>x³+y³=[2a³-3a³+3ab]/2
=> x³+y³=[3ab-a³]/2
Similar questions