Difference between revisions of "1996 AIME Problems"
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== Problem 5 == | == Problem 5 == | ||
| + | Suppose that the roots of <math>x^3+3x^2+4x-11=0</math> are <math>a</math>, <math>b</math>, and <math>c</math>, and that the roots of <math>x^3+rx^2+sx+t=0</math> are <math>a+b</math>, <math>b+c</math>, and <math>c+a</math>. Find <math>t</math>. | ||
[[1996 AIME Problems/Problem 5|Solution]] | [[1996 AIME Problems/Problem 5|Solution]] | ||
Revision as of 14:47, 24 September 2007
Contents
Problem 1
Problem 2
For each real number 
, let 
denote the greatest integer that does not exceed x. For how man positive integers 
is it true that 
and that 
is a positive even integer?
Problem 3
Find the smallest positive integer for which the expansion of 
, after like terms have been collected, has at least 1996 terms.
Problem 4
A wooden cube, whose edges are one centimeter long, rests on a horizontal surface. Illuminated by a point source of light that is centimeters directly above an upper vertex, the cube casts a shadow on the horizontal surface. The area of a shadow, which does not include the area beneath the cube is 48 square centimeters. Find the greatest integer that does not exceed 
.
Problem 5
Suppose that the roots of 
are 
, 
, and 
, and that the roots of 
are 
, 
, and 
. Find 
.
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
A 
rectangular solid is made by gluing together 
cubes. An internal diagonal of this solid passes through the interiors of how many of the cubes?
