Question

if
${a}^{2} + {b}^{2} + {c }^{2} = 44 \: and \: a + b + c = 8. \: find \: the \: value \: of \: {a}^{3} + {b}^{3} + {c}^{3} - 3abc$

Answer 1

I hope this will be write...

Answer 2

Answer:

272

Step-by-step explanation:

A+b+c= 8 and a 2 + b 2 +c 2 = 44, 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 = 8

Squaring on both sides we get,

(a+b+c)² = 8²

a²+b²+c² + 2(ab+bc+ca) = 64

2 (ab+bc+ca) = 20

ab + bc + ca = 10

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

Putting the values we get

8 (44- 10)

8 x 34

272