Question

If $a+b+c=5$ and $ab+bc+ca=10$, then find the value of $a^3+b^3+c^3-3abc$ ?

• A. $30$
• B. $-25$
• C. $24$
• D. $-20$

Answer 1

The correct option is B $-25$

Given,$a+b+c=5$ and $ab+bc+ca=10$

we know that,$(a+b+c{)}^2=a^2+b^2+c^2+2(ab+bc+ca)$ .......1

from $1$ , $a^2+b^2+c^2=5$

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

$a^3+b^3+c^3-3abc=\left(5\right)(5-10)=-25$