Diyadiya
  • Diyadiya
If α≠β but \(α^2=5α−3\) ,\(β^2=5β−3\), then the equation whose roots are \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Diyadiya
  • Diyadiya
I have to find the equation
ash2326
  • ash2326
@Diyadiya did you find \(\alpha\) and \(\beta\) ??
anonymous
  • anonymous
You have to really? really? what if you won't ?

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lgbasallote
  • lgbasallote
ffm to the rescue!!! \m/ hahaha
Diyadiya
  • Diyadiya
@ash2326 Nope i didnt
Diyadiya
  • Diyadiya
\[\alpha+\beta=5\]
ash2326
  • ash2326
\(\alpha \) \(\ne\) \(\beta\) There are two roots of \[\alpha^2=5\alpha-3\] one roots is \(\alpha\) and another is \(\beta\) so \[\alpha+\beta=5\] and \[\alpha\beta=3\]
anonymous
  • anonymous
Your required equation is \(3x^2 -19x+3=0 \)
Diyadiya
  • Diyadiya
Sorry i was afk
ash2326
  • ash2326
so the equation whose roots are \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\) is \[ x^2-(\frac{\alpha}{\beta}\ + \frac{\beta}{\alpha})+\frac{\alpha}{\beta} \times \frac{\beta}{\alpha}=0\]
Diyadiya
  • Diyadiya
@FoolForMath yeah!
Diyadiya
  • Diyadiya
okay Thank you :) @ash2326
ash2326
  • ash2326
Welcome:D
anonymous
  • anonymous
Do you read Mathematics today?
Diyadiya
  • Diyadiya
No ?
Diyadiya
  • Diyadiya
Why?
anonymous
  • anonymous
You should, lots of cute problems in there.
Diyadiya
  • Diyadiya
lol ok
Diyadiya
  • Diyadiya
I still didn't get it how do you find the sum in \[x^2-(\frac{\alpha}{\beta}\ + \frac{\beta}{\alpha})+\frac{\alpha}{\beta} \times \frac{\beta}{\alpha}=0 \]
anonymous
  • anonymous
Do you know: \(a^2+b^2 = (a+b)^2-2 ab \)?
Diyadiya
  • Diyadiya
Yeah
anonymous
  • anonymous
then use it ;)
Diyadiya
  • Diyadiya
Ok
Diyadiya
  • Diyadiya
Thanks
anonymous
  • anonymous
Welcome :) Btw, Sometimes it's good to use that cute head of yours :P I mean Leena's :D

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