Difference between revisions of "1953 AHSME Problems/Problem 23"
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The equation <math>\sqrt {x + 10} - \frac {6}{\sqrt {x + 10}} = 5</math> has: | The equation <math>\sqrt {x + 10} - \frac {6}{\sqrt {x + 10}} = 5</math> has: | ||
− | <math>\textbf{A}</math> an extraneous root between <math>-5</math> and <math>-1</math> | + | <math>\textbf{(A)}</math> an extraneous root between <math>-5</math> and <math>-1</math> |
<math>\textbf{(B)}</math> an extraneous root between <math>-10</math> and <math>-6</math> | <math>\textbf{(B)}</math> an extraneous root between <math>-10</math> and <math>-6</math> |
Revision as of 18:41, 30 April 2018
The equation has:
an extraneous root between
and
an extraneous root between
and
a true root between
and
two true roots
two extraneous roots
We multiply both sides by to get the equation
. We square both sides to get
, or
. We can factor the quadratic as
, giving us roots of
and
. We plug these values in to find that
is an extraneous root and that
is a true root, giving an answer of
.