यदि `x=(4sqrt(15))/(sqrt(5)+sqrt(3))` है तो `(x+sqrt(20))/(x-sqrt(20))+(x+sqrt(12))/(x-sqrt(12))` का मान ज्ञात करें।

Options

A. 1
B. 2
C. `sqrt(3)`
D. `sqrt(5)`

Answer

B

Explanation

`x=(4sqrt(15))/(sqrt(5)+sqrt(3))`
`(x+sqrt(20))/(x-sqrt(20))+(x+sqrt(12))/(x-sqrt(12))=?`
`:. x=(4xxsqrt(5)xxsqrt(3))/(sqrt(5)+sqrt(3))=(2xx(sqrt(5)xxsqrt(12)))/(sqrt(15)+sqrt(3))`
or `(2xxsqrt(20)xxsqrt(3))/(sqrt(5)+sqrt(3))`
`x/(sqrt(12))=(2sqrt(5))/(sqrt(5)+sqrt(3))`
by C-D rule
`(x+sqrt(12))/(x-sqrt(12))=(2sqrt(5)+sqrt(5)+sqrt(3))/(2sqrt(5)-sqrt(5)-sqrt(3))`
`=(3sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))`
`x/(sqrt(20))=(2sqrt(3))/(sqrt(5)+sqrt(3))`
`(x+sqrt(20))/(x-sqrt(20))=(2sqrt(3)+sqrt(5)+sqrt(3))/(2sqrt(3)-sqrt(5)-sqrt(3))`
`=(3sqrt(3)+sqrt(5))/(sqrt(3)-sqrt(5))`
`:. (x+sqrt(12))/(x-sqrt(12))+(x+sqrt(20))/(x-sqrt(20))`
`=(3sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(3sqrt(3)+sqrt(5))/(sqrt(3)-sqrt(5))`
`= (3sqrt(5)+sqrt(3)-3sqrt(3)-sqrt(5))/(sqrt(5)-sqrt(3))`
`=(2sqrt(5)-2sqrt(3))/(sqrt(5)-sqrt(3))=2`