Question

Verify (x x y) -1 = x -1 x y -1 , when x = −/ , y = /

Answer 1

Step-by-step explanation:

Let x=1+a+a

2

+and y=1+b+b

2

. where ∣a∣<1 and ∣b∣<1. Prove that 1+ab+a

2

b

2

+.=

x+y−1

xy

Medium

Solution

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Verified by Toppr

Using C,P, we get

x=1+a+a

2

+.

x=

1−a

1

y=1+b+b

2

+.

y=

1−b

1

and Let P=1+ab+a

2

b

2

+

P=

1−ab

1

and

x+y−1

xy

=

1−a

1

+

1−b

1

−1

1−a

1

×

1−b

1

x+y−1

xy

=

1−b+1−a−1+a+b−ab

1

=

1−ab

1

Since P=

1−ab

1

=

x+y−1

xy

Hence Proved.