Write a pair of irrational numbers whose sum is rational.

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Solution

Let the two irrational numbers be $10 + 2 \sqrt{5}$ and $5 - 2 \sqrt{5}$

Sum of these irrational numbers = $10 + 2 \sqrt{5} + 5 - 2 \sqrt{5}$ = 10 + 5 = 15, which is rational.

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