सिद्ध कीजिए कि - `(1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5`

Options

A. 5
B. 4
C. 3
D. 2

Answer

A

Explanation

`1/(3-sqrt(8))`
`implies1/(3-sqrt(8)xx(3+sqrt(8))/(3+sqrt(8)))implies(3+sqrt(8))/(9-8)`
`implies3+sqrt(8)`
Similarly,
`implies1/(sqrt(8)-sqrt(7))=sqrt(8)+sqrt(7)`
`implies1/(sqrt(7)-sqrt(6))impliessqrt(7)+sqrt(6)`
`implies 1/(sqrt(6)-sqrt(5))=sqrt(6)+sqrt(5)`
`implies1/(sqrt(5)-2)=sqrt(5)+2`
Put vaue in question
`implies (3+sqrt(8))-(sqrt(8)+sqrt(7))+(sqrt(7)+sqrt(6))`
`-(sqrt(6)+sqrt(5))+(sqrt(5)+2)`
`implies 3+sqrt(8)-sqrt(8)-sqrt(7)+sqrt(7)+sqrt(6)-sqrt(6)-sqrt(5)+sqrt(5)+2`
`implies3+2=5`