Question

If x-1/x =1/6,find the value of : x2 +1/ x2 and x3+1/x3. Solution by steps.

Answer 1

We have,

=> (x-1)/x = 1/6
=> x/x - 1/x = 1/6
=> 1 - 1/x = 1/6
=> -1/x = 1/6 - 1
=> 1/x = 1 - 1/6
=> 1/x = (6-1)/6
=> 1/x = 5/6

Now, squaring both sides, we get :-

=> 1/x² = 25/36

Similarly, on cubing both sides, we get :-

=> 1/x³ = 125/216

Then,

=> (x²+1)/x²
=> x²/x² + 1/x²
=> 1 + 25/36
=> 61/36

and,
=> (x³+1)/x³
=> x³/x³ + 1/x³
=> 1 + 125/216
=> 341/216

Hope this helps.