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syed ahmed
:
if x+1/x= root3 then x cube + 1/x cue=?
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May 19, 2014 at 1:55pm
Little Sky
:
Interpretation:[deqn]x+\frac{1}{x}=\sqrt{3};~x^3+\frac{1}{x^3}=?[/deqn] Solution:[deqn]\left( x+\frac{1}{x} \right)^3=\sqrt{3}^3\\\left( x+\frac{1}{x} \right)\left( x+\frac{1}{x} \right)\left( x+\frac{1}{x} \right)=\sqrt{3}^3\\\left( x^2 +2+\frac{1}{x^2}\right)\left( x+\frac{1}{x} \right)=\sqrt{3}^3\\ x^3+2x+\frac{1}{x}+x+\frac{2}{x}+\frac{1}{x^3}=\sqrt{3}^3\\x^3+\frac{1}{x^3}+3x+\frac{3}{x}=\sqrt{3}^3\\x^3+\frac{1}{x^3}+3\left( x+\frac{1}{x}\right)=\sqrt{3}^3\\x^3+\frac{1}{x^3}+3(\sqrt{3})=\sqrt{3}^3\\x^3+\frac{1}{x^3}=\sqrt{3}^3-3\sqrt{3}[/deqn]
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May 19, 2014 at 9:12pm
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