Question

A+b+c= 15 and a 2 + b 2 +c 2 =83, find the value of a 3 +b 3 +c 3 -3abc ?

Answer 1

-(ab+bc+ca)=71
a^3+b^3+c^3-3abc=2310

Answer 2

Answer:

180

Step-by-step explanation:

A+b+c= 15 and a 2 + b 2 +c 2 =83, find the value of a 3 +b 3 +c 3 -3abc  

Consider the formula - a³+b³+c³- 3abc = (a+b+c) (a²+b²+c²-(ab+bc+ca))

We have to find ab+bc+ca

given a+b+c = 15

Squaring on both sides we get,

(a+b+c)² = 15²

a²+b²+c² + 2(ab+bc+ca) = 225

2 (ab+bc+ca) = 142

ab + bc + ca = 71

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

Putting the values we get

15(83-71)

15×12

180