If x + 1/x = 5, find the value of x^5 + 1/x^5

Question

anonymous · Answer

well first find the value of x with the first equation then plug it in and ur good to go..

anonymous · Answer

$$\LARGE\frac{x + 1}{x} = 5 \implies 5x = x + 1 \implies 4x = 1 \implies x = \frac14$$Now, plug it into the second equation.
$$\LARGE\frac{x^5 + 1}{x^5} \implies \frac{(\frac14)^5 + 1}{(\frac14)^5} \implies ?$$

anonymous · Answer

@Calcmathlete  it is x+(1/x) isnt it???

anonymous · Answer

Is it?

anonymous · Answer

i dont know

anonymous · Answer

Not sure...the question was a bit vague...

anonymous · Answer

i thought Calcmathlete was right.. its how i did it

anonymous · Answer

|dw:1343659784187:dw|

That is what I meant.

The question wants me to find the value without finding the value of x...

anonymous · Answer

welll then the prob is just raised to the 5th so whats 5 times its self 5 times

anonymous · Answer

@katiebugg That wouldn't work because if you raise it to the fifth power, it becomes:
$$(x + \frac1x)^5 = 5^5$$

anonymous · Answer

but isnt every thing raised to the fifth except 1 that is but that wouldnt matter cuz its still 1