Question

How to solve this

Answer 1

If \[a \neq b \] but \[a ^{2} = 5a - 3 \] and \[b ^{2} = 5b - 3 \]
then find the equation whose roots are
\[\frac{ a }{ b } and \frac{ b }{ a }\]

Answer 2

@ganeshie8

Answer 3

See:

a quadratic equation with roots \(\alpha\) and \(\beta\) is given by :

\[ax^2 + bx + c = 0\]
iff

\[\alpha + \beta = \cfrac{-b}{a}\]
\[\alpha \beta = \cfrac{c}{a}\]

Answer 4

Yes i know that

Answer 5

Gud now here replace alpha and beta by a/b and b/a

Answer 6

Nope

Answer 7

See:

\[ax^2 + bx + c = 0\]
\[\implies x^2 + \cfrac{b}{a} x + \cfrac{c}{a} = 0\]
\[\implies x^2 - \text{(sum of roots)} x + \text{(product of roots)} = 0\]

Answer 8

But the roots are
\[\frac{ a }{ b } and \frac{ b }{a }\]

Answer 9

Here sum of roots will be:

\[\cfrac{a}{b} + \cfrac{b}{a} = \cfrac{a^2 + b^2}{ab}\]

product of roots will be :

\[\cfrac{a}{b} \cfrac{b}{a} = 1\]

Answer 10

Did you get it upto this step ?

Answer 11

(a+b)^2 -2ab / ab

Answer 12

Yes

Answer 13

This is the sum of roots

sum of roots is :- -b/a

Product of roots is :- c/a

Substituting that gives what i just wrote

Answer 14

no why are you including this c

Answer 15

which "c"