student-name

Nur Iman asked in Maths

How to answer?

Q4. Given that x –  1 x  = 3,

      (a) find the value of x 2  –  1 x 2  .

    Expand  x - 1 x 3  .

      (b) Hence deduce the values of 

              (i)  x 3   - 1 x 3  and

              (ii) ‚Äč x 6   - 1 x 6

Thank You
student-name

Varun Rawat answered this

Dear Student,

Please find below the solution to the asked query :


We have,    x - 1x = 3Squaring both sides, we get      x - 1x2 = 9x2 + 1x2 - 2 × x × 1x = 9x2 + 1x2 - 2 = 9x2 + 1x2 = 11    .....1Squaring the above equation, we get     x2 + 1x22 = 121x4 + 1x4 + 2 × x2 × 1x2 = 121x4 + 1x4 = 119Now, x2 - 1x22 = x4 + 1x4 - 2 × x2 × 1x2 x2 - 1x22 = 119 - 2x2 - 1x22 = 117x2 - 1x2 = ±313     ......2   x - 1x3 = x - 1xx - 1xx - 1x=x - 1xx - 1x2=x - 1xx2 + 1x2 - 2×x×1x=x - 1xx2 + 1x2 - 2=xx2 + 1x2 - 2 - 1xx2 + 1x2 - 2=x3 + 1x - 2x - x - 1x3 + 2x=x3 - 1x3 - 3x + 3x=x3 - 1x3  - 3x - 1xSo, x - 1x3 = x3 - 1x3  - 3x - 1xPut x - 1x = 3 in the above identity, we get    33 =  x3 - 1x3 - 3 × 3x3 - 1x3 = 36From 2, we get  x2 - 1x2 = 313Cubing both sides, we get      x6 - 1x6 - 3×x2×1x2x2 - 1x2 = 35113x6 - 1x6 - 3 × 313 = 35113x6 - 1x6 = 36013Taking   x2 - 1x2 = -313Cubing both sides, we get      x6 - 1x6 - 3×x2×1x2x2 - 1x2 = -35113x6 - 1x6 - 3 × 313 = -35113x6 - 1x6 = -34213



Hope this would clear your doubt.

If you have any other doubts, do let us know about the same and our experts will try to help you out as soon as possible.

Regards