Question

if a + b + c = 9 and a square + b square + c square = 35 find the value of a cube plus b cube plus c cube - 3abc​

Answer 1

Answer:

Given (a + b + c) = 9

Squaring on both the sides, we get

(a + b + c)2 = 92

⇒ a2 + b2 + c2 + 2(ab + bc + ca) = 81

⇒ 35 + 2(ab + bc + ca) = 81

⇒ 2(ab + bc + ca) = 81 – 35 = 46

⇒ ab + bc + ca = 23 → (1)

Recall that a3+b3+c3-3abc = (a + b + c)( a2 + b2 + c2 – ab – bc – ca)

= 9(35 – 23)

= 9(12) = 108

Answer 2

Step-by-step explanation:

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