Question

if a if a + b + c is equal to 10 and a square+ b square + c square =83 find the value of a cube+ bcube + c cube -3abc​

Answer 1

Answer:

a+b+c=10......(1)

squaring both sides in (1)

(a+b+c)²=(10)²

a²+b²+c²+2ab+2bc+2ac=100

83+2(ab+bc+ac)=100

2(ab+bc+ac)=100-83

2(ab+bc+ac)=17

ab+bc+ac=17/2

we know that,

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

=(10) (83-17/2)

=745

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