Question

if a^(-1) / a =7
find a^4+ 1/a^4=?
options:- a)2599
b)2699
c)2709
d)2707

Answer 1

$= > \dfrac{ {a}^{ - 1} }{a} = 7 \\ \\ \\ = > \frac{1}{a \times a} = 7 \\ \\ \\ = > \frac{1}{ {a}^{2} } = 7 \: \: \: \: \: \: \: - - - - - - - - - - ( \: 1 \: ) \\ \\ = > \frac{1}{7} = {a}^{2} \: \: \: \: \: - - - - - - - - - - \: ( \: 2 \: )$







In ( 1 ) , squares on both sides ,



$\huge{(} \small{\dfrac{1}{a {}^{2} } } \: \huge{ )}{ \small{}^{ {}^{ {}^{ {}^{2} } } }} \small{ = ( \pm7) {}^{2} } \\ \\ \\ = > \frac{1}{a {}^{4} } = 49$





In ( 2 ) , square on both sides ,



$({a}^{2}) {}^{2} =( \frac{1}{7} {)}^{2} \\ \\ \\ = > {a}^{4} = \frac{1}{49}$








Adding a⁴ and 1 / a⁴


$\frac{1}{49} + 49 \\ \\ \\ = > \frac{1 + {49}^{2} }{49} \\ \\ \\ = > \frac{1 + 2401 }{49} \\ \\ \\ = > \frac{2402}{49}$