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galina1969 [7]
2 years ago
11

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

Mathematics
1 answer:
Umnica [9.8K]2 years ago
8 0

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

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

____________________________________

\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}  {}^{}  =  \sqrt{100}

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

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

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