Question

if x=√3 +√2 then find value of x^4+1/x^4​

Answer 1

Answer :

x +1/x = √3+√2 +1/(√3+√2) = √3+√2 +

(√3-√2)/(√3+√2)*(√3-√2) =√3+√2 +(√3-√2)/(3-2) = 2√3

On squaring on both sides, we get

${(x + \frac{1}{x} )}^{2} = 12 = >$

${x}^{2} + \frac{1}{ {x}^{2} } + 2 = 12 = >$

${x}^{2} + \frac{1}{ {x}^{2} } = 10$

Now square the above equation on both sides, we get

${( {x}^{2} + \frac{1}{ {x}^{2} })}^{2} = 100 \: = >$

${x}^{4} + \frac{1}{ {x}^{4} } + 2 = 100 = >$

${x}^{4} + \frac{1}{ {x}^{4} } + 2 = 100 = > {x}^{4} + \frac{1}{ {x}^{4}} = 98$

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