Question

If α≠β but \(α^2=5α−3\) ,\(β^2=5β−3\), then the equation whose roots are \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\)

Answer 1

I have to find the equation

Answer 2

@Diyadiya did you find \(\alpha\) and \(\beta\) ??

Answer 3

You have to really? really? what if you won't ?

Answer 4

ffm to the rescue!!! \m/ hahaha

Answer 5

@ash2326 Nope i didnt

Answer 6

\[\alpha+\beta=5\]

Answer 7

\(\alpha \) \(\ne\) \(\beta\)
There are two roots of
\[\alpha^2=5\alpha-3\]
one roots is \(\alpha\) and another is \(\beta\)
so
\[\alpha+\beta=5\]
and
\[\alpha\beta=3\]

Answer 8

Your required equation is \(3x^2 -19x+3=0 \)

Answer 9

Sorry i was afk

Answer 10

so the equation whose roots are \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\) is
\[ x^2-(\frac{\alpha}{\beta}\ + \frac{\beta}{\alpha})+\frac{\alpha}{\beta} \times \frac{\beta}{\alpha}=0\]

Answer 11

@FoolForMath yeah!

Answer 12

okay Thank you :) @ash2326

Answer 13

Welcome:D

Answer 14

Do you read Mathematics today?

Answer 15

No ?

Answer 16

Why?

Answer 17

You should, lots of cute problems in there.

Answer 18

lol ok

Answer 19

I still didn't get it
how do you find the sum in
\[x^2-(\frac{\alpha}{\beta}\ + \frac{\beta}{\alpha})+\frac{\alpha}{\beta} \times \frac{\beta}{\alpha}=0 \]

Answer 20

Do you know: \(a^2+b^2 = (a+b)^2-2 ab \)?

Answer 21

Yeah

Answer 22

then use it ;)

Answer 23

Ok

Answer 24

Thanks

Answer 25

Welcome :) Btw, Sometimes it's good to use that cute head of yours :P I mean Leena's :D