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