Question

(vii) y = x^n(1 - x)^n​

Answer 1

Answer:

Given,

x

n

+y

n

x

n+1

+y

n+1

=

xy

.......... Geometric mean

⇒x

n+1

+y

n+1

=

xy

(x

n

+y

n

)

⇒x⋅x

n

−x

n

⋅x

2

1

⋅y

2

1

=y

n

⋅x

2

1

⋅y

2

1

−y⋅y

n

⇒x

n+

2

1

(

x

2

1

−y

2

1

)=y

n+

2

1

(

x

2

1

−y

2

1

)

⇒(

y

x

)

n+

2

1

=1

⇒(

y

x

)

n+

2

1

=(

y

x

)

0

⇒n+

2

1

=0⇒n=−

2

1