Math, asked by rheaboury, 11 months ago

if X=3+√8 find x²+1/x²​

Answers

Answered by darabutterfly242
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.

Answered by ajay8949
5

\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.}

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