Question

If x=3-2 root 2, find x2+1/x2

Answer 1

Hey mate!

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Given :

$x = 3 - 2 \sqrt{2}$

To find :

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

Solution :

$x = 3 - 2 \sqrt{2} \\ \\ \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2}} \times \frac{3 + 2 \sqrt{2}}{3 + 2 \sqrt{2}} \\ \\ \frac{1}{x} = \frac{3 + 2\sqrt{2} }{(3) {}^{2} - (2 \sqrt{2} ) {}^{2} } \\ \\ \frac{1}{x} = \frac{3 + 2 \sqrt{2} }{9 - 8} \\ \\ \frac{1}{x} = 3 + 2 \sqrt{2}$

Now,

$x + \frac{1}{x} = 3 - \cancel{2 \sqrt{2}} + 3 + \cancel{2 \sqrt{2}} \\ \\ x + \frac{1}{x} = 3 + 3 \\ \\ x + \frac{1}{x} = 6$

Again,

$\bold{on \: squaring \: both \: sides.} \\ \\ (x + \frac{1}{x}) {}^{2} = (6) {}^{2} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } + 2 \times \cancel x \times \frac{1}{ \cancel x} = 36 \\ \\ x {}^{2} + \frac{1}{x {}^{2} }+ 2 = 36 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = 36 - 2 \\ \\ \therefore \boxed{\bold{x {}^{2} + \frac{1}{x {}^{2} } = 34}}$

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Thanks for the question !

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Answer 2

Answer:

x = 3-2√2

x2 = (3-2√2)2 = 9+8-12√2 = 17-12√2

1/x2= 1/17-12√2

Rationalise The Denominator

1*17+12√2 / (17-12√2 ) * (17+12√2) = 17+12√2/289-288 = 17+12√2

Now Add We Get

17-12√2+17+12√2 = 34

So Answer - 34