Question

If a +b+c = 5, ab + ac + bc = 3 and abc = -27, find the value of a^3 + b^3 + c^3​

Answer 1

Answer:

-1

Step-by-step explanation:

Identity!

$(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=a^3+b^3+c^3-3abc$.

We don't have $a^2+b^2+c^2$.

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

∴$a^2+b^2+c^2=25-2\times 3=19$

Now we can go further.

$a^3+b^3+c^3=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)+3abc$

$a^3+b^3+c^3=5\times (19-3)+3\times (-27)=80-81=-1$.

∴Thus, the answer is -1.

Answer 2

hope u will be satisfied with the answer