Difference between revisions of "1991 AHSME Problems/Problem 20"
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The sum of all real <math>x</math> such that <math>(2^x-4)^3+(4^x-2)^3=(4^x+2^x-6)^3</math> is | The sum of all real <math>x</math> such that <math>(2^x-4)^3+(4^x-2)^3=(4^x+2^x-6)^3</math> is | ||
− | (A) 3/ | + | (A) <math>\frac{3}{2}</math> (B) <math>2</math> (C) <math>\frac{5}{2}</math> (D) <math>3</math> (E) <math>\frac{7}{2}</math> |
== Solution == | == Solution == |
Revision as of 17:30, 27 October 2018
Problem
The sum of all real such that is
(A) (B) (C) (D) (E)
Solution
Let , so the equation becomes . Hence , or , or , but for all , so we cannot have ; however, works, giving Thus we have solutions: , whose sum is
See also
1991 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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