Difference between revisions of "1956 AHSME Problems/Problem 41"

(Solution)
(Solution)
 
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Start by plugging in <math>y=2x:</math>
 
Start by plugging in <math>y=2x:</math>
 
<cmath>12x^2 + 2x + 4 = 12x^2 + 4x + 4</cmath>
 
<cmath>12x^2 + 2x + 4 = 12x^2 + 4x + 4</cmath>
The only value that can satisfy this equation is <math>x=0</math> meaning the answer is C
+
The only value that can satisfy this equation is <math>x=0</math> meaning the answer is <math>\boxed{\textbf{(C)}}.</math>
  
-coolmath34
+
-samcool
  
 
==See Also==
 
==See Also==
 
{{AHSME 50p box|year=1956|num-b=40|num-a=42}}
 
{{AHSME 50p box|year=1956|num-b=40|num-a=42}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 13:06, 24 July 2024

Problem 41

The equation $3y^2 + y + 4 = 2(6x^2 + y + 2)$ where $y = 2x$ is satisfied by:

$\textbf{(A)}\ \text{no value of }x \qquad \textbf{(B)}\ \text{all values of }x \qquad \textbf{(C)}\ x = 0\text{ only} \\ \textbf{(D)}\ \text{all integral values of }x\text{ only} \qquad \textbf{(E)}\ \text{all rational values of }x\text{ only}$

Solution

Start by plugging in $y=2x:$ \[12x^2 + 2x + 4 = 12x^2 + 4x + 4\] The only value that can satisfy this equation is $x=0$ meaning the answer is $\boxed{\textbf{(C)}}.$

-samcool

See Also

1956 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 40
Followed by
Problem 42
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All AHSME Problems and Solutions

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