Question

If a+b+c=12, a2+b2+c2=9, a3+b3+c3=6 then find the value of abc
and ab+bc+ca.
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Answer 1

Answer:

abc = 236

abc = 236ab+bc+ca = 135/2

Step-by-step explanation:

(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca)

(ab+bc+ca) = ((12)^2 - 9)/2

= 135/2

We have a result ( better to be remembered ) >

a3+b3+c3 - 3abc

= (a+b+c)(a^2 + b^2 + c^2 - (ab+bc+ca))

= 12 × (9 - 135/2)

= 12 × (-117/2)

= -702

3abc = 6+702 = 708

abc = 708/3 = 236