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Consider Cardano's problem of finding two numbers whose sum is 10 and whose product is 40. a)...

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Basic Math

Consider Cardano's problem of finding two numbers whose sum is10 and whose product is 40.

a) Cardano knew beforehand that no such (real) numbers existed.How did he know? Can you prove it?

b) Solve the system of equations x+y=10 and xy=40 to findCardano's complex solution.

c) Check that this solution does work-that is, thatb the sum ofyour complex numbers is 10 and that their product is 40.

Answer & Explanation Solved by verified expert
3.6 Ratings (510 Votes)
aThese two numbers must be both positive If they are both negative their product could be 40 but then their sum would be a negative number not 10 If they are one    See Answer
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