Question

14. If a + b + c = 15 and a2+ b2+c2=83 then find the value of a3 + b3 + c3 -3abc​

Answer 1

Answer:

The value of a³+b³+c³ is

$180$

Step-by-step explanation:

a+b+c=15,a²+b²+c²=83,a³+b³+c³=x,ab+bc+ca=71 and ab-bc-ca=-71

Substitute the value according to the formulae

Let be [a+b+c]²=a²+b²+c²+2ab+2bc+2ca

[15]²=a²+b²+c²+2[ab+bc+ca]

225=83+2[ab+bc+ca]

225-83/2=ab+bc+ca

ab+bc+ca=71

Let be a³+b³+c³-3abc=[a+b+c][a²+b²+c²-ab-bc-ca]

a³+b³+c³-3abc=[15][83-71]

a³+b³+c³-3abc=180

hence value is 180