



 
Gautam, I looked for an easy way to see this but if there is one it eludes me. I just did it by brute force. I do know that if a and b are roots of x^{2} + px + 1 = 0 then a + b = p and ab = 1. Similarly if c and d are rots of x^{2} + qx + 1 = 0 then c + d = q and cd = 1. Hence
Now expand (a  c)(b  c)(a + d)(b + d) completely and use the sum of the roots and product of the roots above to simplify the expression and verify that its value is c^{2} + d^{2}  a^{2}  b^{2}. Harley  


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