If a + b + c = 5, a3 + b3 + c3 = 85 and abc = 25, then find the value of a2 + b2 + c2 - ab - bc - ca.
Answer & explanation
Correct answer: option 1
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