Question

`\huge\sf\underline{Question}`


`\sf If \: {x}^(2) + (1)/(x ^(2) ) = 34`

`\sf find \: the \: value \: of \: \: \: x + (1)/(x)`
a proper explanation needed :)

Thxx !! ​

Answer 1

`{\qquad\quad\qquad\huge\underline{{\sf Answer}}}`

Here we go ~

`\qquad \sf  \dashrightarrow \: {x}^(2) + \cfrac{1}{ {x}^(2) } = 34`

[ add 2 on both sides ]

`\qquad \sf  \dashrightarrow \: {x}^(2) + \cfrac{1}{ {x}^(2) } + 2 = 34 + 2`

[ form identity : a² + b² + 2ab ]

`\qquad \sf  \dashrightarrow \: {(x)}^(2) + { \bigg(\cfrac{1}{ {x}^{} } \bigg) }^(2) + 2 \sdot(x) \sdot \bigg(\cfrac{1}{x} \bigg) = 36`

[ a² + b² + 2ab = (a + b)² ]

`\qquad \sf  \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^(2) = 36`

`\qquad \sf  \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{} = √( 36)`

`\qquad \sf  \dashrightarrow \: x + \cfrac{1}{x} = \pm 6`

so, the value of required expression is 6

[usually positive value is considered, but if asked the value can be either positive or negative]