Question

if a+b+c=9 and a^2+b^2+c^2 =35,find the value of a^3+b^3+c^3-3abc.

Answer 1

Given a + b + c = 9 and a^2 + b^2 + c^2 = 35.

Let us consider, a + b + c = 9.

On squaring both sides, we get

= > (a + b + c)^2 = (9)^2

= > a^2 + b^2 + c^2 + 2ab + 2bc + 2ca = 81

= > 35 + 2(ab + bc + ca) = 81

= > 2(ab + bc + ca) = 81 - 35

= > 2(ab + ca + ca) = 46

= > ab + bc + ca = 23.

Now,

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

                                                              = (9)(35 - 23)

                                                              = 9(12)

                                                              = 108.



Hope this helps!

Answer 2

here is the solution.........