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Three arithmetic means, three geometric means and three harmonic means are inserted between 1 and 5 . The cubic equation whose roots are 3rd A.M., 2nd G.M. and 1st H.M. is
(a) \( x^{3}-\frac{1}{4}(21+4 \sqrt{5}) x^{2}+5 x-5 \sqrt{5}=0 \)
(c) \( 4 x^{3}-(21+4 \sqrt{5}) x^{2}+(15+21 \sqrt{5}) \)
(b) \( x^{3}-\frac{1}{4}(21+4 \sqrt{5}) x^{2}+\left(5+\frac{21}{4} \sqrt{5}\right) x \) \( -20 \sqrt{5}=0 \)
(d) none of these
\[
-5 \sqrt{5}=0
\]
\( \mathrm{P} \)
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