0 vote
If p = 4 + √15, then find the value of \(\frac{{{p^7} + {p^5} + {p^3} + p}}{{{p^2}}}\)
If p = 4 + √15, then find the value of \(\frac{{{p^7} + {p^5} + {p^3} + p}}{{{p^2}}}\)
1). 31941.61
2). 33841.91
3). 30741.61
4). 38204.53
1 answers
3 vote
⇒ $(\frac{{{p^7} + {p^5} + {p^3} + p}}{{{p^2}}})$ (given)
⇒ $({p^5} + {p^3} + p + \frac{1}{p})$
⇒ $(p = 4 + \surd 15)$
⇒ $(\frac{1}{p} = \frac{1}{{4 + \sqrt {15}}} \times \frac{{4 - \sqrt {15}}}{{4 - \sqrt {15}}} = 4 - \surd 15)$
⇒ $({p^3} = {\left({4 + \sqrt {15}} \right)^3} = 64 + 48\sqrt {15} + 180 + 58.09 = 487.99)$
⇒ $({p^2} = {\left({4 + \sqrt {15}} \right)^2} = 16 + 8\sqrt {15} + 15 = 61.98)$
⇒ $({p^5} = {p^3} \times {p^2} = 487.99 \times 61.98 = 30245.62)$
⇒ $({p^5} + {p^3} + p + \frac{1}{p} = 30245.62+ 487.99 + 4 + \sqrt {15} + 4 - \sqrt {15})$
∴ Answer is 30741.61