यदि `x=3-2sqrt2` हो तो `x^(2)+(1)/(x^(2))` का मान ज्ञात कीजिए:

Explanation

दिया है कि `x=3-2sqrt2`
`:.(1)/(x)=(1)/(3-2sqrt2)=(1)/(3-2sqrt2)xx(3+2sqrt2)/(3+2sqrt2)`
`implies(1)/(x)=(3+2sqrt2)/(3^(2)-(2sqrt2)^(2))=(3+2sqrt2)/(9-8)=3+2sqrt2`
अतः `x^(2)+(1)/(x^(2))=3^(2)+(2sqrt2)^(2)+(3+2sqrt2)^(2)`
`impliesx^(2)+(1)/(x^(2))=3^(2)+(2sqrt2)^(2)-2xx3xx2sqrt2+3^(2)+(2sqrt2)^(2)+2xx3xx2sqrt2`
`impliesx^(2)+(1)/(x^(2))=9+8-12sqrt2+9+8+12sqrt2=34`