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Difference between revisions of "1972 AHSME Problems/Problem 11"

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Because x<sup>2</sup> + y<sup>2</sup> + 16 = 0 has no real solutions, &#8704; sets containing x<sup>2</sup> + y<sup>2</sup> + 16 = 0, no real solutions may exist.
 
Because x<sup>2</sup> + y<sup>2</sup> + 16 = 0 has no real solutions, &#8704; sets containing x<sup>2</sup> + y<sup>2</sup> + 16 = 0, no real solutions may exist.
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&#8756; the solution is <math>\fbox{D}</math>
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– TylerO_1.618
 
– TylerO_1.618
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&#8756; the solution is <math>\fbox{D}</math>
 

Latest revision as of 13:37, 4 February 2022

Problem

The value(s) of $y$ for which the following pair of equations $x^2+y^2+16=0\text{ and }x^2-3y+12=0$ may have a real common solution, are

$\textbf{(A) }4\text{ only}\qquad \textbf{(B) }-7,~4\qquad \textbf{(C) }0,~4\qquad \textbf{(D) }\text{no }y\qquad \textbf{(E) }\text{all }y$

Solution

Because x2 + y2 + 16 = 0 has no real solutions, ∀ sets containing x2 + y2 + 16 = 0, no real solutions may exist.

∴ the solution is $\fbox{D}$


– TylerO_1.618

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