Question

Need help pls give me help plea

Answer 1

`527`

Explanation:

`\mathrm{Solution:}\\x+(1)/(x)=5\\\mathrm{Squaring\ both\ sides,}\\\mathrm{or,\ }x^2+2.x.(1)/(x)+(1)/(x^2)=25\ \ \ \ \\\mathrm{or,\ }x^2+2+(1)/(x^2)=25\\\mathrm{or,\ }x^2+(1)/(x^2)=23\\`

`\mathrm{Squaring\ both\ sides,}\\(x^2+(1)/(x^2))^2=23^2\\\mathrm{or,\ }x^4+2x^2(1)/(x^2)+(1)/(x^4)=529\\\\\mathrm{or,\ }x^4+2+(1)/(x^4)=529\\\\\mathrm{or,\ }x^4+(1)/(x^4)=527`

Answer 2

(D) 527

Explanation:

`\textsf{To\;find\;the\;value\;of\;\;$x^4+(1)/(x^4)$,\;given\;\;$x+(1)/(x)=5$,}\\\\\textsf{begin\;by\;squaring\;both\;sides\;of\;the\;equation:}`

`\begin{aligned}\left(x+(1)/(x)\right)^2&=5^2\\\\\left(x+(1)/(x)\right)\left(x+(1)/(x)\right)&=25\\\\x^2+(x)/(x)+(x)/(x)+(1)/(x^2)&=25\\\\x^2+1+1+(1)/(x^2)&=25\\\\x^2+(1)/(x^2)&=23\end{aligned}`

Square both sides of the equation again:

`\begin{aligned}\left(x^2+(1)/(x^2)\right)^2&=23^2\\\\\left(x^2+(1)/(x^2)\right)\left(x^2+(1)/(x^2)\right)&=529\\\\x^4+(x^2)/(x^2)+(x^2)/(x^2)+(1)/(x^4)&=529\\\\x^4+1+1+(1)/(x^4)&=529\\\\x^4+(1)/(x^4)&=527\\\\\end{aligned}`

Therefore, the correct answer option is (D) 527.