# Composition xoy=(x-1)(y-1)+1 Calculate (`sqrt1` /2)o(`sqrt2` /2)o----o(`sqrt2009` /2)

Asked on by ruals

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to notice that if you replace 1 for `y` in the given law of composition yields:

`xo1 = (x - 1)(1 - 1) + 1 => xo1 = (x - 1)*0 + 1 => xo1 = 1`

You need to notice that if you replace 1 for `x` in the given law of composition yields:

`1oy = (1 - 1)(y - 1) + 1 => 1oy = 1`

Hence, you should come up with the following substitution, such that:

`sqrt1/2osqrt2/2osqrt3/2 = x`

`(sqrt5/2)o(sqrt6/2)o ... o(sqrt2009/2) = y`

Replacing x and y in the given expression `(sqrt1/2)o(sqrt2/2)o(sqrt3/2)o(sqrt4/2)o(sqrt5/2)o ... o(sqrt2009/2)` yields:

`xo(sqrt4/2)oy = xo(2/2)oy => xo(sqrt4/2)oy = (xo1)oy`

`xo(sqrt4/2)oy = 1oy => xo(sqrt4/2)oy = 1`

Hence, evaluating the given expression, using the given law of composition, yields `(sqrt1/2)o(sqrt2/2)o(sqrt3/2)o(sqrt4/2)o(sqrt5/2)o ... o(sqrt2009/2) = 1` .

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