Question

.Prove that: 13−√8-1√8−√7+ 1√7−√6-1√6−√5+ 1√5−2=5

Answer 1

I'm sure the question must be:

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

Ans.

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.