Question

find the value of a3+b3+c3-3abc if a+b+c =5 and a2+b2+c2=29

Answer 1

Given a + b + c = 5 and a^2 + b^2 + c^2 = 29.

On squaring both sides, we get
 
= > (a + b + c)^2 = (5)^2

= > a^2 + b^2 + c^2 + 2ab + 2bc + 2ca = 25

= > a^2 + b^2 + c^2 + 2(ab + bc + ca) = 25

= > 29 + 2(ab + bc + ca) = 25

= > 2(ab + bc + ca) = 25 - 29

= > ab + bc + ca = -2

Now,

We know that a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 +c^2 - ab - bc - ca)

                                                               = (5)(29 + 2)

                                                               = 155.


Hope this helps!

Answer 2

Hi,

Please see the attached file!



Thanks