Question

Prove that 1/3-√8 -1/√8-√7 +1/√7-√6 -1/√6-√5 +1/√5-2=5

Answer 1

1/3-√8-1/√8-√7+1/√7-√6-1/√6-√5+1/√5-2=5
Now,
1/3-√8 = 3+√8,
1/√8-√7 = √8+√7,
1/√7-√6 = √7+√6,
1/√6-√5 = √6+√5,
1/√5-2 = √5+2
∴ 1/3-√8-1/√8-√7+1/√7-√6-1/√6-√5+1/√5-2
= 3+√8-√8-√7+√7+√6-√6-√5+√5+2
=3+2 = 5
Hence proved.

Answer 2

1/3-√8-1/√8-√7+1/√7-√6-1/√6-√5+1/√5-2=5

Now,

1/3-√8 = 3+√8,

1/√8-√7 = √8+√7,

1/√7-√6 = √7+√6,

1/√6-√5 = √6+√5,

1/√5-2 = √5+2

∴ 1/3-√8-1/√8-√7+1/√7-√6-1/√6-√5+1/√5-2

= 3+√8-√8-√7+√7+√6-√6-√5+√5+2

=3+2 = 5

Hence proved.