Solve $\frac{(6.9)^3+(2.7)^3+(5.8)^3-3×6.9×2.7×5.8}{(6.9)^2+(2.7)^2+(5.8)^2-(6.9)(2.7)-(2.7)(5.8)-(5.8)(6.9)}$
Answer & explanation
Correct answer: option 4
a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)
$\frac{(6.9)^3+(2.7)^3+(5.8)^3-3×6.9×2.7×5.8}{(6.9)^2+(2.7)^2+(5.8)^2-(6.9)(2.7)-(2.7)(5.8)-(5.8)(6.9)}$
= \(\frac{(6.9 + 2.7 + 5.8)(6.9^2 + 2.7^2 + 5.8^2 - (6.9)(2.7)-(2.7)(5.8)-(5.8)(6.9)}{(6.9)^2+(2.7)^2+(5.8)^2-(6.9)(2.7)-(2.7)(5.8)-(5.8)(6.9)}\)
= (6.9 + 2.7 + 5.8) = 15.4