Question

SE
13. If x = 9+4/5, find the value of x²+1/x²
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Answer 1

Given that,

$x = \frac{9 + 4}{5} = \frac{13}{5} \\ {x}^{2} = \frac{169}{25}$

To find,

${x}^{2} + \frac{1}{ {x}^{2} } = ?$

Calculations,

${x}^{2} = \frac{169}{25} \\ \frac{1}{ {x}^{2} } = \frac{25}{169} \\ {x}^{2} + \frac{1}{ {x}^{2} } = \frac{25}{169} + \frac{169}{25} \\ {x}^{2} + \frac{1}{ {x}^{2} } = \frac{625 + 28561}{4225} \\ = \frac{29186}{4225} \\ = 6.9$

Final answer,

${x}^{2} + \frac{1}{ {x}^{2} } = 6.9$

hope it helps to you☺️

Answer 2

Answer .

322

Explanation:

x²= (9+4+√5)² = ( 81+80+72√5)=161+72√5=161+72√5 .

x² +1/x²= 161+72√5+1/(161+72√5) = (25921+25920+23284√5+1/(161+72√5)= ( 51482+23184√5/161+72√5= 322 .