If a + b + c = 5, a³ + b³ + c³ = 85 and abc = 25, then find the value of a² + b² + c² - ab - bc - ca.

2

We know that,

a³ + b³ + c³ - 3 × a × b × c = (a + b + c)(a2 + b2+ c2 - ab - bc - ca)

We have,

a + b + c = 5

a³ + b³ + c³  = 85

a × b × c = 25

= (a + b + c)(a² + b²+ c² - ab - bc - ca) = a³ + b³ + c³ - 3 × a × b × c

= 5 × (a² + b²+ c² - ab - bc - ca) = 85 - (3 × 25)

= (a² + b²+ c² - ab - bc - ca) = 10/5 = 2