# Some Number Problems

IF it is given that a+b=c+d AND ab=cd, does it imply that a=c and b=d or a=d and b=c?

Note by Keshav Gupta
4 years, 5 months ago

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Squaring the 1st expression and subtracting the 2nd from the 1st and rearranging leads to the result: (a+c)(a-c) = (d+b)(d-b) But we already know that a-c = d-b, so we have (a+c) = (d+b), or a = d. Similarly for a = c, etc.

- 4 years, 5 months ago

Thankyou very much Sir! I researched about it and found other ways to prove it as well.. One would be to assume they are the roots of a polynomial, they should be equal because they would be the roots of the same polynomial. Thanks for you time again! :)

- 4 years, 5 months ago