Question

If a+b+c=5 and if ab+bc+ca=10
Than prove that a^3+b^3+c^3-3abc=-25

Answer 1

we know , 
a³ + b³ + c³ -3abc = (a + b + c )(a² + b² + c² -ab -bc-ca) 
now , 
a + b + c = 5 ab + bc + ca = 10 
(a + b + c)² = a² + b² + c² +2(ab + bc+ca)(5)² -2×10 = a² + b² + c² a² + b² + c² =5 
hence ,
a³ + b³ +c³ -3abc = ( a + b + c )(a² + b² + c² -ab- bc-ca)
=( 5)( 5 - 10) = 5 × (-5) = -25 
hence proved//