`1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+1/(sqrt(5)-2)-1/(sqrt(8)-sqrt(7))+1/(3-sqrt(8))` का मान ज्ञात करें।

Options

A. 0
B. 1
C. 5
D. 7

Answer

C

Explanation

`1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+`
`1/(sqrt(5)-2)-1/(sqrt(8)-sqrt(7))+1/(3-sqrt(8))`
`implies` Rationalising
`implies(sqrt(7)+sqrt(6))/((sqrt(7)+sqrt(6))(sqrt(7)-sqrt(6)))-1/((sqrt(6)-sqrt(5)))`
`xx((sqrt(6)+sqrt(5))/((sqrt(6)+sqrt(5))))+(sqrt(5)+sqrt(4))/((sqrt(5)-sqrt(4))(sqrt(5)+sqrt(4)))`
`-((sqrt(8)+sqrt(7)))/((sqrt(8)+sqrt(7))(sqrt(8)-sqrt(7)))+((sqrt(9)+sqrt(8)))/((sqrt(9)+sqrt(8))(sqrt(9)-sqrt(8)))`
`implies (sqrt(7)+sqrt(6))/1-((sqrt(6)+sqrt(5)))/1+`
`((sqrt(5)+sqrt(4)))/1-((sqrt(8)+sqrt(7)))/1+(sqrt(9)+sqrt(8))/1`
`implies sqrt(7)+sqrt(6)-sqrt(6)-sqrt(5)+sqrt(5)+sqrt(4)-sqrt(8)-`........
`sqrt(7)+sqrt(9)+sqrt(8)`
`implies sqrt(4)+sqrt(9)=2+3=5`