Question

If p+1/p =√3 ,prove that p^3+1/p^3=0​

Answer 1

$\small \bf \pink{hey \: mate \: here \: is \: ur \: an s\: } \\ \\ \small \bf \pink{ \huge \: solution} \\ \\ \small \bf \pink{p + \frac{1}{p} = \sqrt{3} } \\ \\ \small \bf \pink{now} \\ \\ \small \bf \pink{ {p}^{3} + \frac{1}{ {p}^{3} } = 0 } \\ \\ \small \bf \pink{we \: know \: that} \\ \\ \small \bf \pink{ p + \frac{1}{p} = \sqrt{3} } \\ \\ \small \bf \pink{cubing \: on \: both \: sides} \\ \\ \small \bf \pink{again \: we \: know \: that} \\ \\ \small \bf \pink{(a + b)^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) } \\ \\ \small \bf \pink{ {p}^{3} + \frac{1}{ {p}^{3} } + 3 \times p \times \frac{1}{p}(p + \frac{1}{p} ) = \sqrt{3}^{3} } \\ \\ \\ \small \bf \pink{ {p}^{3} + \frac{1}{p^{3}} + 3 \times 1( \sqrt{3} ) = 3 \sqrt{3} } \\ \\ \small \bf \pink{ {p}^{3} + \frac{1}{ {p}^{3} } + 3 \sqrt{3} = 3 \sqrt{3} } \\ \\ \small \bf \pink{ {p}^{3} + \frac{1}{ {p}^{3} } = 3 \sqrt{3} - 3 \sqrt{3} } \\ \\ \small \bf \pink{ {p}^{3} + \frac{1}{ {p}^{3} } = 0 \: \: \: proved }$