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To find two numbers that multiply to 1764 and add up to 84, we first factorize 1764 to its prime factors: 2 x 2 x 3 x 3 x 7 x 7. Then, we look for pairs of factors that multiply to 1764. The pair that adds up to 84 is 42 and 42, as 42 x 42 = 1764 and 42 + 42 = 84. Therefore, the two numbers are 42 and 42.