Question

if X=3+√8 find x²+1/x²​

Answer 1

Answer:

Step-by-step explanation:

x = 3+ √8

x = (3+√8)(3-√8) / (3-√8)

x = (9 -8) / (3-√8)

x = 1/ (3 -√8)

Or we can write 1/x = (3-√8)

Put the value and find out

x² +(1/x²) = x² + (1/x)²

So x² + 1/ x² = (3 +√8)² + (3 -√8)²

= 9+6√8+8 + 9–6√8+8

= 34. Ans.

Answer 2

$\huge\bold\red{Given\::-}$

$x = 3 + \sqrt{8}$

$\huge\bold\blue{To\:Find\::-}$

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

$\huge\mathfrak\orange{Solution\::-}$

=> $(3 + \sqrt{8} ) {}^{2} + \frac{1}{(3 + \sqrt{8}) {}^{2} }$

=> $(3 {}^{2} + { \sqrt{8} }^{ \: 2} + 2(3)( \sqrt{8}) \: + \frac{1}{(3 {}^{2} + { \sqrt{8} }^{ \: 2} + 2(3)( \sqrt{8}) \: }$

=> $9 + 8 + 6 \sqrt{8} + \frac{1}{9 + 8 + 6 \sqrt{8}}$

=> $17 + 6 \sqrt{8} + \frac{1}{17 + 6 \sqrt{8} }$

rationalising the denominator of

=> $\frac{1}{17 + 6 \sqrt{8} }$

=> $\frac{1}{17 + 6 \ \sqrt{8} } \times \frac{17 - 6 \sqrt{8} }{17 - 6 \sqrt{8} }$

=> $\frac{17 - 6\sqrt{8}}{17 {}^{2} - (6 \sqrt{8)^{2} } }$

=> $\frac{17 - 6 \sqrt{8} }{289 - 288}$

=> $\frac{17 - 6 \sqrt{8} }{1}$

=> 17 - 6√8

Now,

17 + 6√8 + 17 - 6√8

= 34

$\huge\fcolorbox{blue}{yellow}{please\:mark\:as\:brainliest.}$