Question

If x² + 1/x² = 102, then x -1/x =
a) 10
b) 8
c) 13
d) 12

Answer 1

`\quad \huge \quad \quad \boxed{ \tt \:Answer }`

`\qquad \tt \rightarrow \:A. \:\: 10`

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`\large \tt Solution \: :`

`\qquad \tt \rightarrow \: {x}^(2) + \cfrac{1}{ {x}^(2) } = 102`

[ subtract 2 from both sides ]

`\qquad \tt \rightarrow \: {x}^(2) + \cfrac{1}{ {x}^(2) } - 2 = 102 - 2`

`\qquad \tt \rightarrow \: {x}^(2) + \cfrac{1}{ {x}^(2) } - \bigg( 2 \sdot x \sdot \cfrac{1}{x} \bigg)= 100`

[ 2 can written like that, as they cancel out each other ]

Apply Identity [ a² + b² -2ab = (a - b)² ]

`\qquad \tt \rightarrow \: \bigg (x - \cfrac{1}{x} \bigg) {}^(2) = 100`

`\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = √(100)`

`\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = 10`

Answered by : ❝ AǫᴜᴀWɪᴢ ❞