How does this equation yield into the following

Asked Jul 09 '18 at 19:50

Active Jul 09 '18 at 20:55

Viewed 53 times

$\frac{(a^2 + b^2)} {(ab + 1)} = k$

becomes

$x^2-kb \cdot x + (b^2 - k) = 0$

in an example I am attempting to understand, can you please clarify how the quadratic equation follows from the equation above?

edited Jul 09 '18 at 20:55

max_zorn

asked Jul 09 '18 at 19:50

Is this Vieta jumping? – Dr. Sonnhard Graubner Jul 09 '18 at 19:50
Yes, this a step in the overall problem – Jul 09 '18 at 19:51
see here https://brilliant.org/discussions/thread/vieta-root-jumping-2/ – Dr. Sonnhard Graubner Jul 09 '18 at 19:52
1

I suppose $x=a$. – Angina Seng Jul 09 '18 at 19:55
@Dr.SonnhardGraubner what I am not understanding is how the equation is derived in order to get to the lemma – Jul 09 '18 at 19:59
@LordSharktheUnknown yeah, x = a when the equation is fixed for b and k and manipulated for a – Jul 09 '18 at 20:00
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Try this: (1) multiply both sides by $ab+1$. (2) substract $kab+k$ from both sides. – Clement C. Jul 09 '18 at 20:08

0 Answers0