`1/(sqrt((12-sqrt(140))))-1/(sqrt((8-sqrt(60))))-2/(sqrt(10+sqrt(84)))` का मान ज्ञात करें।

Options

A. 0
B. 1
C. 2
D. 3

Answer

A

Explanation

`1/(sqrt((12-sqrt(140))))-1/(sqrt((8-sqrt(60))))`
`2/(sqrt((10+sqrt(84))))`
`implies1/(sqrt(12-sqrt(4xx35)))-1/(sqrt(8-sqrt(4xx15)))`
`-2/(sqrt(10+sqrt(4xx21)))`
`implies1/(sqrt(12-2sqrt(35)))-1/(sqrt(8-2sqrt(15)))-2/(sqrt(10+2sqrt(21)))`
`implies 1/(sqrt((sqrt(7))^(2)+(sqrt(5))^(2)-2sqrt(7)sqrt(5)))-1/(sqrt((sqrt(5)^(2)+(sqrt(3)^(2)-sqrt(5)sqrt(3)))-`
`2/(sqrt((sqrt(7))^(2)+(sqrt(3))^(2)-2sqrt(7)sqrt(3)))`
`implies1/(sqrt((sqrt(7)-sqrt(5))^(2)))1/(sqrt((sqrt(5)-sqrt(3))^(2)))-2/(sqrt((sqrt(7)+sqrt(3))^(2)))`
`implies1/(sqrt(7)-sqrt(5))-1/(sqrt(5)-sqrt(3))-2/(sqrt(7)-sqrt(3))`
Relationlizing in above equation.
`implies1/(sqrt(7)-sqrt(5))xx(sqrt(7)+sqrt(5))/(sqrt(7)+sqrt(5))-1/(sqrt(5)-sqrt(3))xx`
`(sqrt(5)+sqrt(3))/(sqrt(5)+sqrt(3))-2/(sqrt(7)+sqrt(3))xx(sqrt(7)-sqrt(3))/(sqrt(7)-sqrt(3))`
`implies (sqrt(7)+sqrt(5))/2-((sqrt(5)+sqrt(3)))/2-((sqrt(7)-sqrt(3)))/2`
`implies sqrt(7)+sqrt(5)-sqrt(5)-sqrt(3)-sqrt(7)+sqrt(3)/2`
`implies0`