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If the samller number is x, then

x2 + (x + 1)2 = 41

ie x2 + x2 + 2x + 1 = 40

ie 2x2 + 2x - 40 = 0

or x2 + x - 20 = 0

so that x2 + 5x - 4x - 20 = 0

then x(x + 5) -4(x + 5) = 0

or (x + 5)(x - 4) = 0

which implies that x = -5 or x = 4

Since x is positive, x = 4.

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