1don't you think u should this by ur own??:)
If a,b are the roots of x2+px+1=0 and c,d are the roots of x2+qx+1=0 then show that q2-p2=(a-c)(b-c)(a+d)(b+d)
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4 Answers
1(a-c)(b-c)(a+d)(b+d)
={(a-c)(b+d)}{(b-c)(a+d)}
=(ad-bc)(bd-ac) [ as ab=cd=1]
=d2-b2+c2-a2
=(c2+2cd+d2)-(a2+2ab+b2) [ ab=cd=1]
=(c+d)2-(a+b)2
=q2-p2
[as c+d=-q; a+b=-p]
1I've proved it from RHS to LHS.
Someone please prove in the reverse way.
