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Let the two numbers be represented by a and b.

Then ab = 20, so b = 20/a.

a + b = 10, substituting for b gives, a + 20/a = 10

Multiplying throughout by a, and making the equation equal to zero :-

a2 - 10a + 20 = 0

Solving using the quadratic formula.

a = [10 ± √(102 - 4x20)] ÷ 2 = [10 ± √20] ÷ 2 = 5 ± √5 = 5 ± 2.2361 (4dp)

The two numbers are therefore 5 + 2.2361 = 7.2361 and 5 - 2.2361 = 2.7639

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