Question

lf lf a+b+c=9 and a^2+b^2+c^2=35, find the value of ( a^3+b^3+c^3-3abc).

Answer 1

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Answer 2

Answer:

108

Step-by-step explanation:

A+b+c= 9 and a 2 + b 2 +c 2 = 35, 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 = 9

Squaring on both sides we get,  

(a+b+c)² = 9²  

a²+b²+c² + 2(ab+bc+ca) = 81

2 (ab+bc+ca) = 46

ab + bc + ca = 23

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

Putting the values we get  

9 (35 - 23)  

9 x 12

108