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X-1/x=6 ,evaluate x²+ 1/x² |
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Answer» x+ x1 =6 On squaring both sides we get,\begin{lgathered}{(x + \frac{1}{x}) }^{2} = {6}^{2} \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2(x)( \frac{1}{x} ) = 36 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 36 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 34\end{lgathered} (x+ x1 ) 2 =6 2 x 2 + x 2 1 +2(x)( x1 )=36x 2 + x 2 1 =36−2x 2 + x 2 1 =34 Identity I used ={(a + B)}^{2} = {a}^{2} + {b}^{2} + 2ab(a+b) 2 =a 2 +b 2 +2ab\boxed{ \textsf{ \RED{ Hence\:answer\:is\:34 }}} Henceansweris34 |
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