Question

$if \: \alpha \: and \: \beta \: are \: real \: and \: \alpha {}^{2} and \: - \beta \: are \: the \: roots \: of \: the \: equation \: {a}^{2} x {}^{2} + x + (1 - a {}^{2} ) = 0 \: where \: a > 1 \: then \: \beta {}^{2} =$

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Answer 1

Answer:

Hey mate this is your answer......

Answer 2

Answer:

α+β,α

2

+β

2

,α

3

+β

3

are in G.P.

∴(α

2

+β

2

)

2

=(α+β)(α

3

+β

3

)

∴α

4

+β

4

+2α

2

β

2

=α

4

+β

4

+α

3

β+αβ

3

∴α

2

β

2

−α

3

β−αβ

3

+α

2

β

2

=0

∴α

2

β(β−α)−αβ

2

(β−α)=0

∴(α

2

β−αβ

2

)(β−α)=0

∴αβ(α−β)(β−α)=0

∴αβ(α−β)

2

=0

∴α=0 or β=0 or α−β=0