Difference between revisions of "1980 AHSME Problems/Problem 8"
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<cmath> a^2+ab+b^2=0.</cmath> | <cmath> a^2+ab+b^2=0.</cmath> | ||
− | By the quadratic formula and checking the discriminant, we see that this has no real solutions. Thus the answer is <math>\boxed{\text{(A)none}}</math>. | + | By the quadratic formula and checking the discriminant (imagining one of the variables to be constant), we see that this has no real solutions. Thus the answer is <math>\boxed{\text{(A)none}}</math>. |
== See also == | == See also == | ||
{{AHSME box|year=1980|num-b=7|num-a=9}} | {{AHSME box|year=1980|num-b=7|num-a=9}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 15:59, 20 March 2018
Problem
How many pairs of non-zero real numbers satisfy the equation
Solution
We hope to simplify this expression into a quadratic in order to find the solutions. To do this, we find a common denominator to the LHS by multiplying by .
By the quadratic formula and checking the discriminant (imagining one of the variables to be constant), we see that this has no real solutions. Thus the answer is .
See also
1980 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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 | ||
All AHSME Problems and Solutions |
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