यदि `x=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))` और `y=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))` है तो `x^(3)+y^(3)` का मान ज्ञात करें।

Options

A. 950
B. 930
C. 650
D. 970

Answer

D

Explanation

`x=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))`
`y=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))`
`:. x=1/y`
`y=1/ximplies xy=1`
`:. x+y=(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))/1`
`implies (3+2-2sqrt(6)+3+2+2sqrt(6))/1=10`
`implies (x+y)^(3)+x^(3)+y^(3)+3xy(x+y)`
`implies (10)^(3)=x^(3)+y^(3)+3xx1(10)`
`implies x^(3)+y^(3)=1000-30=970`