1.

If `x=3-2sqrt2," find "x^(2)+1/x^(2)`

Answer» We have, `x=3-2sqrt2`
`:. 1/x=1/(3-2sqrt2)xx(3+2sqrt2)/(3+2sqrt2)`
`=(3+2sqrt2)/((3)^(2)+(2sqrt2)^(2))=(3+2sqrt2)/(9-8)=3+2sqrt2`
Thus,`x^(2)+1/x^(2)=(3-2sqrt2)^(2)+(3+2sqrt2)^(2)`
`=(3)^(2)+(2sqrt2)^(2)-2xx3xx2sqrt2+(3)^(2)+(2sqrt2)^(2)+2xx3xx2sqrt2`
`=9+8-12sqrt2+9+8+12sqrt2=34`


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