Question

If x=3+2√2 then find the value of x²+1/x²

Answer 1

Answer:

Given that,

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

And we have to calculate the value of

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

So,

Put the value of x in the expression

${x}^{2} + \frac{1}{ {x}^{2} } \\ = {(3 + 2 \sqrt{2} )}^{2} + \frac{1}{( {3 + 2 \sqrt{2)} }^{2} } \\ = 9 + 8 + 12 \sqrt{2} + \frac{1}{9 + 8 + 12 \sqrt{2} } \\ = 17 + 12 \sqrt{2} + \frac{1}{17 + 12 \sqrt{2} } \times \frac{17 - 12 \sqrt{2} }{17 - 12 \sqrt{2} } \\ = 17 + 12 \sqrt{2} + ( \frac{17 - 12 \sqrt{2} }{289 - 288} \\ = 17 + 12 \sqrt{2} + \frac{17 - 12 \sqrt{2} }{1} \\ = 17 + \cancel{ 12 \sqrt{2}} + 17 - \cancel{12 \sqrt{2}} \\ = 17 + 17 \\ = 34$

So,

After simplification the value of given expression will be 34 .