Question

verify that (x×y)-¹ -x-¹×y-¹ when x- -2/3 and y- -3/5​

Answer 1

Answer:

Expanding, we get

n

C

1

xy

n−1

+2

n

C

2

x

2

y

n−2

+3

n

C

3

x

3

y

n−3

+...n

n

C

n

x

n

=x[

n

C

1

y

n−1

+2

n

C

2

x

1

y

n−2

+3

n

C

3

x

2

y

n−3

+...n

n

C

n

x

n−1

]

=x[

dx

d(y+x)

n

] ...(keeping y constant.)

=x(n(x+y)

n−1

)

Now x+y=1,

Hence we get

x(n)

=nx