Question

x=5+3√2 find x^2+1/x^2​

Answer 1

Given:-

• x=5+3√2

To find:-

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

Solution:-

x² = ( 5+3√2 )²

x² = 25 + 18 + 30√2.

x² = 43 + 30√2.

And ,

$\frac{1 }{ { x }^{2} } = \frac{1}{ {(5 + 3 \sqrt{2}) }^{2} }$

$\frac{1}{ { x }^{2} } = \frac{1}{(43 + 30 \sqrt{2} )}$

So, now

${x}^{2} + \frac{1}{ {x}^{2} } = (43 + 30 \sqrt{2} ) + \frac{1}{(43 + 30 \sqrt{2} ) }$

${x}^{2} + \frac{1}{ {x}^{2} } = \frac{ {(43 + 30 \sqrt{2} )}^{2} + 1 }{43 + 30 \sqrt{2} }$

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