1.

If x = 4+2√2, then find (x-8+8/x).

Answer»

\(x = 4 + 2\sqrt 2\)

\(\frac 1x = \frac1{4 + 2\sqrt 2} = \frac {4 - 2\sqrt 2}{(4 + 2\sqrt 2) (4 - 2\sqrt 2)}\)

\(= \frac {4 - 2\sqrt 2}{16 - 8}\)

\(= \frac{4 - 2\sqrt 2}8\)

\(\therefore x - 8 + \frac 8x = 4 + 2\sqrt 2 - 8 + 4 - 2\sqrt2 = 0\)



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