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Let the numbers be a and b: ab=196 and a+b=35, so b=35-a and a(35-a)=196; 35a-a^2=196; a^2-35a+196=0.

Factors of 196 (=2^2*7^2) are (14,14), (2,98), (4,49), (28,7). The last pair add up to 35, so the factorisation is (a-7)(a-28)=0 and a and b are 7 and 28.

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