analyze the product
(a-3)(a-2)-56/(55)²
do it fast
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Put a-2 = x then a-3 = x-1
The given equation can be written as x(x-1) = 56/(55x55)
x^2 -x = (55+1)/(55x55) = 1/55 + 1/55^2
x^2 - 1/55^2 - x - 1/55 = 0
(x + 1/55)(x- 1/55) - 1 (x+ 1/55) = 0
(x+1/55)(x - 1/55 -1) = 0
(x + 1/55)(x- 56/55) = 0
x = -1/55 or x = 56/55
i.e., a -2 = -1/55 or a-2 = 56/55
a = 109/55 or a= 166/55
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