Question

a+b+c =7 and a3 +b3+c3-3abc =175 find the value of ab+bc+ca?​

Answer 1

Answer:

Given:

⇒ a + b + c = 7

⇒ a3 + b3 + c3 - 3abc = 175

Formula Used:

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

then,

(a + b + c)2 = (a2 + b2 + c2 + 2ab + 2bc + 2ca)

Calculation:

(a + b + c)2 = (a2 + b2 + c2 + 2ab + 2bc + 2ca)

⇒ 49 - 2(ab + bc + ca) = (a2 + b2 + c2) ----(1)

Now,

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

⇒ 175 = 7 × [49 - 2(ab + bc + ca) - ab - bc - ca]

⇒ 3(ab + bc + ca) = 24

⇒ ab + bc + ca = 8

∴ Required value of ab + bc + ca is 8 Ans.