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baldbrain
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Homework Statement
If ##x## is a rational function of ##y##, such that (ax2 + bx + c)y + (a'x2 bx' + c') = 0
prove that (ac' - a'c)2 = (ab' - a'b)(bc' -b'c)
Homework Equations
The quadratic formula
The Attempt at a Solution
This equation can be rewritten as:
(ay + a')x2 (by + b')x (cy +c') = 0
Since x is rational, the discriminant of the above quadratic in ##x## is a perfect square.
(by + b')2 - 4(ay + a')(cy + c') is a perfect square.
(b2 - 4ac)y2 + [2bb' - 4(ac' + a'c)]y + (b'2 - 4a'c') is a perfect square.
(b2 - 4ac)y2 + [2bb' - 4(ac' + a'c)]y + (b'2 - 4a'c') = λ2
,where λ is an integer
That's all I reckon. How to proceed?
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