Difference between revisions of "2021 AMC 12A Problems/Problem 2"
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==Problem== | ==Problem== | ||
| − | + | Under what conditions is <math>\sqrt{a^2+b^2}=a+b</math> true, where <math>a</math> and <math>b</math> are real numbers? | |
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| + | <math>\textbf{(A) }</math> It is never true. | ||
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| + | <math>\textbf{(B) }</math> It is true if and only if <math>ab=0</math>. | ||
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| + | <math>\textbf{(C) }</math> It is true if and only if <math>a+b\ge 0</math>. | ||
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| + | <math>\textbf{(D) }</math> It is true if and only if <math>ab=0</math> and <math>a+b\ge 0</math>. | ||
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| + | <math>\textbf{(E) }</math> It is always true. | ||
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==Solution== | ==Solution== | ||
| − | + | {{solution}} | |
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==See also== | ==See also== | ||
{{AMC12 box|year=2021|ab=A|num-b=1|num-a=3}} | {{AMC12 box|year=2021|ab=A|num-b=1|num-a=3}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 15:22, 11 February 2021
Problem
Under what conditions is 
true, where 
and 
are real numbers?
It is never true.
It is true if and only if 
.
It is true if and only if 
.
It is true if and only if and .
It is always true.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 2021 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 1 |
Followed by Problem 3 |
| 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 | |
| All AMC 12 Problems and Solutions | |
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