Question

Find the value of a^3+b^3+c^3-3abc when a+b+c=10 and a^2+b^2+c^2=83

Answer 1

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Answer 2

Answer:

745

Step-by-step explanation:

A+b+c= 10 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 = 10

Squaring on both sides we get,

(a+b+c)² = 10²

a²+b²+c² + 2(ab+bc+ca) = 100

2 (ab+bc+ca) = 17

ab + bc + ca = 17/2

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

Putting the values we get

10 ( 83- 17/2)

10 x 74.5

745