1966 AMC 12 Problem 10

Attempt Problem 10 of the 1966 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1966 AMC 12 solutions, or check the answer key.

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10.

If the sum of two numbers is

1

and their product is

1,

then the sum of their cubes is, where

i=\sqrt{-1}:

2

-2-\dfrac{3\sqrt3i}{4}

0

-\dfrac{3\sqrt3i}{4}

-2

Use

u^3+v^3=(u+v)^3-3uv(u+v)

Substitute the given sum and product directly

If the numbers are

u,

and

v,

then

\begin{aligned} u^3+v^3 &=(u+v)^3-3uv(u+v)\\ &=1^3-3=-2. \end{aligned}

Therefore, the correct answer is E.

Problem 10 in other years