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

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asked Apr 7, 2023 197k views

1 Answer

Utopalex · Answer 1 · 2023-04-13T17:57:47+0000

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

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

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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 ❞