Question

State the whether given statement is true or false

If $a+b+c=5$ & $ab+bc+ca=10$, the prove that $a^3+b^3+c^3-3abc=-25$.

• A. True
• B. False

Answer 1

The correct option is A True

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

$a^3+b^3+c^3-3abc$

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

$=\left(5\right)\times ({(a+b+c)}^2-2ab-2bc-2ca-ab-bc-ca)$

$=5\times (5^2-3(ab+bc+ca))$

$=5\times (25-3\times 10)$

$=5\times (25-30)$

$=5\times -5=-25$

Hence proved