Question

if x is equal to 6 minus root 35 find the value of x square + 1 upon x square ​

Answer 1

If :

$x = 6 - \sqrt{35}$

Find :

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

Now,

${x}^{2} = {(6 - \sqrt{35}) }^{2}$

$= 36 - 12 \sqrt{35} + 35$

$= 71 - 12\sqrt{35}$

Then,

$\frac{1}{ {x}^{2} } = \frac{1}{ {(71 - 12 \sqrt{35}) } }$

Rationalising the denominator,

$\frac{1}{71 - 12\sqrt{35} } \times \frac{71 + 12\sqrt{35} }{71 + 12\sqrt{35} \: }$

$= \frac{71 + 12 \sqrt{35} }{5041 - 5040} = 71 + 12\sqrt{35}$

Putting the values in the equation,

=

$71 - 12\sqrt{35} + 71 + 12\sqrt{35}$

= 71+71 = 142

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Answer 2

the value of of x²+1/x²=142.....