1Great.....could u pls post ur solution?
(√5+2)1/3-(√5-2)1/3 is
a. Irrational no. b. Prime no.
c. Rational no. d. Natural no.
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6 Answers
1\small see\ the\ given\ no\ is\ the\ root\ of\ the\ equation\\ x^3+3x-4=0\\ we\ can\ see\ that\ 1\ is\ also\ the\ root\ of \ the\ above\\ so\ we\ have \\ x=(\sqrt{5}+2)^{\frac{1}{3}}-(\sqrt{5}-2)^{\frac{1}{3}}=1\\ &\ 1\ is\ a\ rational\ &\ a\ natural\ no...
1@deepansh, we can take the given equation as
p-q=x
then cubing both sides,
x3=p3-q3-3pq(p-q)
So, we get, x3-3x-4=0.