if a*a + b*b + c*c + d*d =762
ab + cd = 260
ac + bd = 365
ad + bc = 244
find abcd
(Sorry can't write the squared of a, b, c, nor d)

Question

if a*a + b*b + c*c + d*d =762
   ab + cd = 260
   ac + bd = 365
   ad + bc = 244
find abcd
(Sorry can't write the squared of a, b, c, nor d)

anonymous · Answer

You have 4 equations with 4 variables. Do you need to solve this in the hand? Or are you allowed to use CAS-tools? If you are allowed to use CAS-tools, check out wolframalpha. http://www.wolframalpha.com/input/?i=a*a%2Bb*b%2Bc*c%2Bd*d%3D762%2C+a*b%2Bc*d%3D260%2C+a*c%2Bb*d%3D365%2C+a*d%2Bb*c%3D244 There is 4 different solutions to the problem, as you can see. But if you need to solve this in the hand then you can the System of linear equations. https://en.wikipedia.org/wiki/System_of_linear_equations