Question

If A +1÷A=5, find the value of A4-1÷A4

Answer 1

Answer:

±115√21

Step-by-step explanation:

$A + \frac{1}{A} = 5\\\\Squaring\: both\: Sides\\\\A^{2} + \frac{1}{A^2} + 2 = 25\\\\A^{2} + \frac{1}{A^2} = 23\\\\(A - \frac{1}{A})^2 = A^{2} + \frac{1}{A^2} - 2\\\\(A - \frac{1}{A})^2 = 23 - 2\\\\(A - \frac{1}{A})^2 = 21\\\\(A - \frac{1}{A}) = \pm \sqrt21$

To find

$A^4 - \frac{1}{A^4}\\\\= (A^{2} + \frac{1}{A^2} )(A^2 - \frac{1}{A^2} )\\\\= (A^2 + \frac{1}{A^2})(A+\frac{1}{A})(A -\frac{1}{A} )\\\\=(23) \times (5) \times (\pm\sqrt{21} )\\\\= \pm 115\sqrt{21}$