Question

If a + b + c =5 and ab + bc +ca = 10 , Prove that a³ + b³ + c³ - 3abc = -25

Answer 1

Hey!!!...here is ur answer

As we know that..
a^3+b^3+c^3 - 3 a b c = (a+b+c)(a^2+b^2+c^2 - a b - b c - a c)

And also know that

(a + b + c)^2 = a^2+ b^2+ c^2+ 2ab + 2bc + 2ca

(5)^2= a^2+ b^2+ c^2+2 (10)

a^2+ b^2+ c^2=5

Now...

a^3+b^3+c^3 - 3 a b c = (a+b+c)(a^2+b^2+c^2 - a b - b c - a c)

a^3+b^3+c^3 - 3 a b c =(5)[5-(10)]


a^3+b^3+c^3 - 3 a b c =5×(-5)

a^3+b^3+c^3 - 3 a b c =-25 HENCE PROVED

Hope it will help you