Difference between revisions of "1954 AHSME Problems/Problem 40"
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<math>a^3+\frac{1}{a^3}=0</math> | <math>a^3+\frac{1}{a^3}=0</math> | ||
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+ | ==Solution 3== | ||
+ | <math>(a+\frac{1}{a})=\sqrt{3}</math> | ||
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+ | <math>a^{2}+2+\frac{1}{a^{2}}=3 \Rightarrow a^{2}+\frac{1}{a^{2}}=1</math> | ||
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+ | <math>(a^{3}+\frac{1}{a^{3}})=(a+\frac{1}{a})(a^{2}-1+\frac{1}{a^{2}}) \Rightarrow (a^{3}+\frac{1}{a^{3}})=\sqrt{3}(1-1) \Rightarrow \fbox{C}</math> |