Question

Find the value of √a+x + √a-x / √a+x - √a-x , if x=2ab / 1+b²​

Answer 1

Answer:

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Answer 2

Given equations are:

bx+ay=a

2

+b

2

.....(1)

ax−by=0 .....(2)

Now re-arranging both the equation in ax+by+c=0 form:

bx+ay−(a

2

+b

2

)=0 ....(3)

ax−by+0=0 .....(4)

From equation (3) and (4) will get

a

1

=b,b

1

=a,c

1

=−(a

2

+b

2

)

a

2

=a,b

2

=−b,c

2

=0

Now applying cross multiplication:

b

1

c

2

−b

2

c

1

x

=

c

1

a

2

−c

2

a

1

y

=

a

1

b

2

−a

2

b

1

1

(b)(0)−(−b)(−a

2

−b

2

)

x

=

(−a

2

−b

2

)a−0(b)

y

=

b(−b)−a(a)

1

⇒

0+b(−a

2

−b

2

)

x

=

(−a

2

−b

2

)a−0

y

=

−a

2

−b

2

1

⇒

b(−a

2

−b

2

)

x

=

(−a

2

−b

2

)a

y

=

−a

2

−b

2

1

⇒

b(−a

2

−b

2

)

x

=

−a

2

−b

2

1

⇒x=b

⇒

(−a

2

−b

2

)a

y

=

−a

2

−b

2

1

⇒y=a

Hence, x−y⇒b−a