Question

If a+b+c=5 andab+bc+ca=10 then find the value of a3+b3+c3-3abc

Answer 1

Note that :

$(a + b + c)^{3} = a^{3} + 3a^{2}(b+c) + 3a(b+c)^{2} + (b + c)^{3}$

$= a^{3} + b^{3} + c^{3} + 3a^{2}b + 3a^{2}c + 3ab^{2} + 3ac^{2} + 3bc^{2} + 3b^{2}c + 6abc$

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

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

$\therefore a^{3} + b^{3} + c^{3} - 3abc = (a + b + c)^{3} - 3(a + b + c)(ab + bc + ca)$

$= 5^{3} - 3(5)(10) = 125 - 150 = \underline{\underline{-25}}.$

I hope I haven't made any errors. If this is good, please mark as brainliest, thanks :)