यदि `a=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))` और `b=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))` तो `(a^(2))/b+(b^(2))/a` का मान क्या होगा?

Options

A. 1030
B. 970
C. 1025
D. 930

Answer

B

Explanation

Given
`:' a=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)),b=(sqrt(3)-sqrt(2))/(sqrt(3)-sqrt(2))`
to find `(a^(2))/b+(b^(2))/a=?`
`implies (a^(3)+b^(3))/(ab)=?`
`implies ((a+b)^(3)-3ab(a+b))/(ab)=?`
`implies a+b=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))+(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))`
`implies ((sqrt(3)-sqrt(2))^(2)+(sqrt(3)+sqrt(2))^(2))/(sqrt(3)^(2)-sqrt(2)^(2))`
`implies(2(sqrt(3)^(2)+sqrt(2)^(2)))/1`
`implies 2xx(5)`
`implies a+b=10`
Again
`implies axxb=((sqrt(3)-sqrt(2)))/((sqrt(3)+sqrt(2)))xx((sqrt(3)+sqrt(2)))/((sqrt(3)-sqrt(2)))`
`implies ab=1`
`implies ((a+b)^(3)-3ab(a+b))/(ab)`
`implies (10^(3)-3xx1xx10)/1`
`implies 1000-30=970`