Difference between revisions of "1960 AHSME Problems/Problem 39"
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==See Also== | ==See Also== | ||
{{AHSME 40p box|year=1960|num-b=38|num-a=40}} | {{AHSME 40p box|year=1960|num-b=38|num-a=40}} | ||
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Revision as of 19:21, 17 May 2018
Problem
To satisfy the equation ,
and
must be:
Solution
First, note that and
. Cross multiply both sides to get
Subtract both sides by
to get
From the quadratic formula,
If
is real, then
is imaginary because
is negative.
If
is not real, where
and
, then
evaluates to
. As long as
, the expression can also be imaginary because a real number squared will be a real number.
From these two points, the answer is
.
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 38 |
Followed by Problem 40 | |
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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
All AHSME Problems and Solutions |