If all solutions to a*x^2+2h*xy + b*y^2 = 1 and c*x^2+2g*xy + d*y^2 = 1 are rational, prove that (ad-bc)^2+4(ag-ch)*(bg-dh) is the square of a rational

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If all solutions to a*x^2+2h*xy + b*y^2 = 1 and c*x^2+2g*xy + d*y^2 = 1 are rational, prove that (ad-bc)^2+4(ag-ch)*(bg-dh) is the square of a rational

Answered Same DayDec 22, 2021

Answer To: If all solutions to a*x^2+2h*xy + b*y^2 = 1 and c*x^2+2g*xy + d*y^2 = 1 are rational, prove that...

David answered on Dec 22 2021
117 Votes
1. If all solutions to and are rational, prove
that ( ) ( )( ) is the square of a rational.
Sol:
Let(


)




The equations become,
We have three simultaneous equations,
For a solution to exist for the first two...
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