Question

if x=√5+2,then find the value of x²+1/x²​.
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Answer 1

Step-by-step explanation:

x² + 1/x²

putting the value of x , we get

(√5+2)²+ 1/(√5+2)²

using the identity of (a+b)² = a²+b²+2ab

(√5)²+(2)²+2*√5*2+1/(√5)²+(2)²+2*√5*2

5+4+4√5+1/5+4+4√5

9+4√5+1/9+4√5

taking LCM

(9+4√5)(9+4√5)+1/9+4√5

$\frac{(9+4√5)(9+4√5)+1}{9 + \sqrt[45]{?} }$

$\frac{9(9 + \sqrt[4]{5) } + \sqrt[4]{5}(9 + \sqrt[4]{5}) }{9 + \sqrt[4]{5} }$

$\frac{81 + \sqrt[36]{5} + \sqrt[36]{5} +16 \times 5 }{9 + \sqrt[4]{5} }$

$\frac{81 + \sqrt[72]{5} + 80}{9 + \sqrt[4]{5} }$

$\frac{161 + \sqrt[72]{5} }{9 + \sqrt[4]{5} }$

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Answer 2

Answer:

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