Question

If a+b+c=5 and ab+bc+ca=10 , then prove that a3+b3+c3= -25?

Answer 1

a ³ + b ³ + c ³ = 3abc = -25

L.H.S = a ³ + b ³ + c 3=³ 
(a+b+c)(a ² + b ² + c ² - ab - bc - ca )
5 [ (a+b+c)² -3(ab+bc+ca) ]
5 [ (5)² - 3 (10)]
5(25-30)
5x - 5
-25

R.H.S = -25

L.H.S = R.H.S

HENCE ITS PROVED