Question

If p+1/p=√3,provr that p^3+1/p^3=0​

Answer 1

$\small \bf \pink{hey \: mate \: here \: is \: ur \: ans} \\ \\ \small \bf \pink{ \huge \: solution} \\ \\ \small \bf \pink{p + \frac{1}{p} = \sqrt{3} } \\ \\ \small \bf \pink{now} \\ \\ \small \bf \pink{p^{3} + \frac{1}{ {p}^{3} } = 0 } \\ \\ \small \bf \pink{given \: that} \\ \\ \small \bf \pink{p + \frac{1}{p} = \sqrt{3} } \\ \\ \small \bf \pink{cubing \: on \: both \: sides} \\ \\ \small \bf \pink{ {p}^{3} + \frac{1}{ {p}^{3} } + 3 \times p \times \frac{1}{p}(p + \frac{1}{ p} ) = { \sqrt{3} }^{3} } \\ \\ \small \bf \pink{ {p}^{3} + \frac{1}{ {p}^{3} } + 3 \times 1( \sqrt{3}) = 3 \sqrt{3} } \\ \\ \small \bf \pink{ {p}^{3} + \frac{1}{ {p}^{3} } + 3 \sqrt{3} = 3 \sqrt{3} } \\ \\ \small \bf \pink{ {p}^{3} + \frac{1}{ {p}^{3} } = 3 \sqrt{3} - 3 \sqrt{3} } \\ \\ \small \bf \pink{ {p}^{3} + \frac{1}{ {p}^{3} } = 0 \: \: \: proved }$