2018 AMC 10A Problems/Problem 10
Contents
Problem
Suppose that real number satisfies What is the value of ?
Solution 1
We let ; in other words, we want to find . We know that Thus, .
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Solution 2
Let , and . Solving for the constants in terms of x, a , and b, we get , and . Subtracting the second equation from the first gives us . Difference of squares gives us . Since we want to find , and we know , we get , so
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Solution 3
We can substitute for , thus turning the equation into . Moving the to the other side and squaring gives us , solving for gives us 25/4. We substitute this value into the expression they asked us to evaluate giving 8.
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Video Solution (HOW TO THINK CREATIVELY!)
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Video Solutions
Video Solution 1
https://youtu.be/ba6w1OhXqOQ?t=1403
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Video Solution 2
https://youtu.be/zQG70XKAdeA ~ North America Math Contest Go Go Go
Video Solution 3
Video Solution 4
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See Also
2018 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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All AMC 10 Problems and Solutions |