If a+b+c=5 and ab +bc+ca=10, then prove that a^3 +b^3 +c^3 – 3abc= - 25.
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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//
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