Question

the value of a+✓a^2-b^2/a-✓a^2-b^2 + a-✓a^2-b^2/a+✓a^2+b^2​

Answer 1

Answer:

x=

a

2

+b

2

−

a

2

−b

2

a

2

+b

2

+

a

2

−b

2

Applying componendo and dividendo,

⇒

x−1

x+1

=

a

2

−b

2

a

2

+b

2

Squaring both sides :

⇒(

x−1

x+1

)

2

=

a

2

−b

2

a

2

+b

2

⇒(x

2

+2x+1)(a

2

−b

2

)=(a

2

+b

2

)(x

2

−2x+1)

=a

2

x

2

+2a

2

x+a

2

−b

2

x

2

−2b

2

x−b

2

=a

2

x

2

−2a

2

x+a

2

+b

2

x

2

−2b

2

x+b

2

⇒2a

2

x−b

2

x

2

−b

2

=−2a

2

x

2

+b

2

x

2

+b

2

on 4a

2

x=2b

2

x

2

+2b

2

2a

2

x=b

2

(x

2

+1)

⇒b

2

=

x

2

+1

2a

2

x

Hence, proved