If `m + (1)/(m) = sqrt3`, then find the simpliest value of (i) `m^(2) + (1)/(m^(2))` and (ii) `m^(3) + (1)/(m^(3))`:

If `m + (1)/(m) = sqrt3`, then find the simpliest value of (i) `m^(2)

1.	If `m + (1)/(m) = sqrt3`, then find the simpliest value of (i) `m^(2) + (1)/(m^(2))` and (ii) `m^(3) + (1)/(m^(3))`:
Answer» (i) `m^(2) + (1)/(m^(2)) = (m)^(2) + ((1)/(m))^(2)` `= (m + (1)/(m))^(2) -2.m. (1)/(m) = (sqrt3)^(2) -2 = 3 -2 =1` `:. m^(2) + (1)/(m^(2)) = 1` (ii) `m^(3) + (1)/(m^(3)) = (m)^(3) + ((1)/(m))^(3) = (m + (1)/(m))^(3) -3.m. (1)/(m) (m + (1)/(m))` `= (sqrt3)^(3) -3 xx sqrt3 = 3 sqrt3 - 3 sqrt3 = 0` `:. m^(3) + (1)/(m^(3)) = 0`

If `x = 2 + sqrt3, y = 2 - sqrt3`, then find the simpliest value of (a) `x - (1)/(x)`, (b) `y^(2) + (1)/(y^(2))`, (c) `x^(3) - (1)/(x^(3))`, (d) `xy + (1)/(xy)`
If `m + (1)/(m) = sqrt3`, then find the simpliest value of (i) `m^(2) + (1)/(m^(2))` and (ii) `m^(3) + (1)/(m^(3))`:
The simpliest value of `(sqrt5 (sqrt(3 - sqrt5)))/(sqrt2 + sqrt(7 - 3 sqrt5))` isA. 1B. 5C. 10D. None of these
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