Question

30. if a + b + c = 5 and ab + bc + ca =10, then find the value of a3 + b3 + c3 3abc.

Answer 1

15 answerrrrrrrrrrrrrrrrrrrrrrr

Answer 2

Answer:

$\bold{- 25}$

Step-by-step explanation:

$a + b + c = 5 \\ \\ (a + b + c)^2 = 5^2 \\ \\ = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac = 25 \\ \\ = a^2 + b^2 + c^2 + 2(ab + bc + ac) = 25 \\ \\ = a^2 + b^2 + c^2 + 2 \times 10 = 25 \\ \\ = a^2 + b^2 + c^2 + 20 = 25 \\ \\ a^2 + b^2 + c^2 = 25 - 20 = 5$

 $\\ \\ \\ (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ac) = a^3 + b^3 + c^3 - 3abc \\ \\ = (a + b + c)(a^2 + b^2 + c^2 - (ab + bc + ac)) = a^3 + b^3 + c^3 - 3abc \\ \\ = 5(5 - 10) = a^3 + b^3 + c^3 - 3abc \\ \\ = 5 \times (-5) = a^3 + b^3 + c^3 - 3abc \\ \\ = \bold{- 25} = a^3 + b^3 + c^3 - 3abc \\ \\ \\ \therefore\ a^3 + b^3 + c^3 - 3abc = \bold{- 25}$

$\\ \\ \\ Hope\ this\ may\ be\ helpful. \\ \\ Please\ mark\ my\ answer\ as\ the\ \bold{brainliest}\ if\ this\ may\ be\ helpful. \\ \\ Thank\ you.\ Have\ a\ nice\ day. \\ \\ \\ \#adithyasajeevan$