Difference between revisions of "2024 AMC 10B Problems/Problem 13"

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==Problem==
 
==Problem==
Positive integers <math>x</math> and <math>y</math> satisfy the equation <math>\sqrtx + \sqrty = \sqrt{1183}</math>. What is the minimum possible value of <math>x+y</math>.
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Positive integers <math>x</math> and <math>y</math> satisfy the equation <math>\sqrt{x} + \sqrt{y} = \sqrt{1183}</math>. What is the minimum possible value of <math>x+y</math>.
  
 
<math>\textbf{(A) } 585 \qquad\textbf{(B) } 595 \qquad\textbf{(C) } 623 \qquad\textbf{(D) } 700 \qquad\textbf{(E) } 791</math>
 
<math>\textbf{(A) } 585 \qquad\textbf{(B) } 595 \qquad\textbf{(C) } 623 \qquad\textbf{(D) } 700 \qquad\textbf{(E) } 791</math>

Revision as of 01:02, 14 November 2024

Problem

Positive integers $x$ and $y$ satisfy the equation $\sqrt{x} + \sqrt{y} = \sqrt{1183}$. What is the minimum possible value of $x+y$.

$\textbf{(A) } 585 \qquad\textbf{(B) } 595 \qquad\textbf{(C) } 623 \qquad\textbf{(D) } 700 \qquad\textbf{(E) } 791$

Solution 1

(Not yet conclusive plz add more stuff) $\sqrt{1183} = 13 \sqrt7 = 6\sqrt7 + 7\sqrt7 = \sqrt{252} + \sqrt{343}$. $252 + 343 = \boxed{\textbf{(B) }595}$

See also

2024 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
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 10 Problems and Solutions

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