`((sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3)))^(2)+((sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3)))^(2)` के बराबर है?

Options

A. 64
B. 62
C. 66
D. 68

Answer

B

Explanation

`((sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3)))^(2)implies((sqrt(5)+sqrt(3))^(2))/((sqrt(5)-sqrt(3))^(2))`
`implies (5+3+2sqrt(15))/(5+3-2sqrt(15))implies(8+2sqrt(15))/(8-2sqrt(15))`
`implies(4+sqrt(15))/(4-sqrt(15))`
Similarly: `((sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3)))^(2)=(4-sqrt(15))/(4+sqrt(15))`
Thus, the expression
`implies(4+sqrt(15))/(4-sqrt(15))+(4-sqrt(15))/(4+sqrt(15))`
`implies (16+15+8sqrt(15)+16+15-8sqrt(15))/((16-15))`
`implies62`