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the product of the sum and the difference of two numbers is 105 . find the two numbers.

Sagot :

(a+b)(a-b) = 105

105 = 3 * 5 * 7

So the possible pairs of sums and differences are:
1 * 105, a + b = 105, a - b = 1, a = 53, b = 52
3 * 35, a + b = 35, a - b = 3, a = 19, b = 16
5 * 21, a + b = 21, a - b = 5, a = 13, b = 8
7 * 15, a + b = 15, a - b = 7, a = 11, b = 4

So (a,b) = {(53,52), (19,16), (13,8), (11,4)}