Question

If x = 4 - √ 5 find the value of x2+1/x2

Answer 1

$\huge\tt{\bold{\underline{\underline{Question᎓}}}}$

If x = 4 - √ 5 find the value of x2+1/x2

$\huge\tt{\bold{\underline{\underline{Answer᎓}}}}$

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Given :x=4-√5

To find :x^2+1/x^2

$\bold{ = > \frac{ {x}^{2} + 1 }{ {x}^{2} }}$

$\bold{= > \frac{ {(4 - \sqrt{5} ) }^{2} + 1}{ {(4 - \sqrt{5} )}^{2} }}$

$\bold{= > \frac{ {(4)}^{2} + {( \sqrt{5} )}^{2} - 2 \times 4 \times \sqrt{5} + 1 }{ {(4)}^{2} + {( \sqrt{5} )}^{2} - 2 \times 4 \times \sqrt{5} }}$

$\bold{= > \frac{16 + 5 - 8 \sqrt{5} + 1 }{16 + 5 - 8 \sqrt{5} }}$

$\bold{= > \frac{11 - 8 \sqrt{5} + 1 }{11 - 8 \sqrt{5} }}$

We can also write this in separate form:

$= > \frac{11 - 8 \sqrt{5} }{11 - 8 \sqrt{5} } + \frac{1}{11 - 8 \sqrt{5} }$

$= > \frac{1}{11 - 8 \sqrt{5} } \:$

$\bold{\red{= \frac{1}{11 - 8 \sqrt{5} } }}$

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