यदि `a=(sqrt(5)+1)/(sqrt(5)-1),b=(sqrt(5)-1)/(sqrt(5)+1)` है। तो `((a^(2)+ab+b^(2)/(a^(2)-ab+b^(2))` का मान ज्ञात करें।

Options

A. `3/4`
B. `4/3`
C. `3/5`
D. `5/3`

Answer

B

Explanation

`a+b=(sqrt(5)+1)/(sqrt(5)-1)+(sqrt(5)-1)/(sqrt(5)+1)`
`implies((sqrt(5)+1)^(2)+(sqrt(5)-1)^(2))/((sqrt(5)-1)(sqrt(5)+1))`
`implies (2[(sqrt(5))^(2)+1])/(5-1)=(2(5+1))/4=3`
`a.b=(sqrt(5)+1)/(sqrt(5)-1)xx(sqrt(5)-1)/(sqrt(5)+1)=1`
Put vaue in expression
`implies (a^(2)+ab+b^(2))/(a^(2)-ab+b^(2))=((a+b)^(2)-ab)/((a+b)^(2)-3ab)`
`(3^(2)-1)/(3^(2)-3)=(9-1)/(9-3)=4/3`