If a= 2+ √52- √5 and b =2- √52+ √5 , find a – b
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3
As a=
2−
5
2+
5
, so,
a
2
=
(2−
5
)
2
(2+
5
)
2
=
9−4
5
9+4
5
And as b=
2+
5
2−
5
, then,
b
2
=
(2+
5
)
2
(2−
5
)
2
=
9+4
5
9−4
5
Now,
a
2
−b
2
=
9−4
5
9+4
5
−
9+4
5
9−4
5
=
(9+4
5
)(9−4
5
)
(9+4
5
)
2
−(9−4
5
)
2
=
81−80
81+80+72
5
−81−80+72
5
=144
5
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