# Difference between revisions of "1985 AIME Problems"

m (USA AIME 1985 Problems moved to 1985 AIME Problems) |
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[[1985 AIME Problems/Problem 2 | Solution]] | [[1985 AIME Problems/Problem 2 | Solution]] | ||

==Problem 3== | ==Problem 3== | ||

+ | Find <math>c</math> if <math>a</math>, <math>b</math>, and <math>c</math> are positive integers which satisfy <math>c=(a + bi)^3 - 107i</math>, where <math>i^2 = -1</math>. | ||

+ | [[1985 AIME Problems/Problem 3 | Solution]] | ||

− | |||

==Problem 4== | ==Problem 4== | ||

## Revision as of 10:22, 3 December 2006

## Contents

## Problem 1

Let , and for let. Calculate the product .

## Problem 2

When a right triangle is rotated about one leg, the volume of the cone produced is . When the triangle is rotated about the other leg, the volume of the cone produced is . What is the length (in cm) of the hypotenuse of the triangle?

## Problem 3

Find if , , and are positive integers which satisfy , where .