यदि `x=3+sqrt(8)` तब `x^(4)+(1)/(x^(4))`, का मान ज्ञात कीजिए ।

Explanation

प्रश्नानुसार, `" " x=3+sqrt(8) rArr (1)/(x)=(1)/(3+ sqrt(8))`
`" " (1)/(3+sqrt(8))xx(3-sqrt(8))/(3-sqrt(8))=(3-sqrt(8))/((3)^(2)-(sqrt(8))^(2))=(3-sqrt(8))/(9-8)=3-sqrt(8)`
अब `" " x+(1)/(x)=(3+sqrt(8))+(3-sqrt(8))=6`
इसलिए `" " x^(2)+(1)/(x^(2))=(x +(1)/(x))^(2)-2=(6)^(2)-2=36-2=34`
तथा `x^(4)+(1)/(x^(4))=(x^(2)+(1)/(x^(2)))^(2)-2=(34)^(2)-2=(34)^(2)-2=1156-2=1154`