Question

If x=3+2√2 find the value of x^2+1/ x^2

Answer 1

x = 3+2√2

1/x = 1/3+2√2

= 1/3+2√2 × 3-2√2/3-2√2

= 3-2√2/(3+2√2)(3-2√2)

= 3-2√2/{3²-(2√2)²}

= 3-2√2/{9-4(2)}

= 3-2√2/9-8

= 3-2√2

x+1/x = 3+2√2+3-2√2

= 6

x²+1/x² = (x+1/x)²-2(x)(1/x)

= 6²-2

= 36-2

= 34

Hope it helps...

Answer 2

Answer:

⇒34

Step-by-step explanation:

Given ,

⇒x = 3 + 2√2

Hence ,

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

$= > \frac{1}{(3 + 2 \sqrt{2}) } \times \frac{(3 - 2 \sqrt{2} )}{(3 - 2 \sqrt{2}) }$

$= > \frac{(3 - 2 \sqrt{2} )}{(3) ^{2} - (2 \sqrt{2})^{2}}$

$= > \frac{(3 - 2 \sqrt{2}) }{(9 - 8)} = 3 - 2 \sqrt{2}$

Hence ,

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

$= > (x + \frac{1}{x} )^{2} = 6^{2} = 36$

$= > x ^{2} + \frac{1}{x^{2} } + 2 \times x \times \frac{1}{x} = 36$

$= > (x^{2} + \frac{1}{x^{2} } ) = 36 - 2$

Hence ,

$= > (x^{2} + \frac{1}{x^{2} } ) = 34$