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What are two numbers that you multiply to get 49 and add to 28?
Wiki User
∙ 12y ago
77
Arianna Blick
nqobile muzari
Wiki User
∙ 12y agoa + b = 28
ab = 49
Being a perfect square of a Prime number, 49 can only be factored out to 7 *7. Unfortunately, 7 + 7 is not equal to 28, so there is no integer solution to this problem. This means we'll need to work it out the long way:
a + b = 28
b = 28 - a
ab = 49
a(28 - a) = 49 - substituting b
28a - a2 = 49 - expanding
a2 - 28a = -49 - moving "a" terms to the left
a2 - 28a + 142 = 142 - 49 - completing the square
(a - 14)2 = 196 - 49 - solving for a
a - 14 = ± √147
a = 14 ± √147
a = 14 ± 7√3
So the numbers are 14 + 7√3 and 14 - 7√3
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