यदि `a=3-2sqrt(2)` तो `a^(2)+(1)/(a^(2))` का मान ज्ञात करें।

Explanation

प्रश्न से, `a=3-2sqrt(2)`
`therefore (1)/(a)=(1)/(3-2sqrt(2))=(1)/(3-2sqrt(2))xx(3+2sqrt(2))/(3+2sqrt(2))=(3+2sqrt(2))/(3^(2)-(2sqrt(2))^(2))`
`=(3+2sqrt(2))/(9-8)=3+2sqrt(2)`
अब, `a^(2)+(1)/(a^(2))=(3-2sqrt(2))^(2)+(3+2sqrt(2))^(2)`
`=3^(2)+(2sqrt(2))^(2)-2xx3xx2sqrt(2)+3^(2)+(2sqrt(2))^(2)+2xx3xx2sqrt(2)`
`=9+8-12sqrt(2)+9+8+12sqrt(2)=34`