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  • If x=9-4?5,then find the value of x^2+1/x^2

If x=9-4?5,then find the value of x^2+1/x^2

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best_answer

Given,
x=9-4sqrt5------(1)
On squaring,we get
x^2=81+80-72sqrt5
x^2=161-72sqrt5-------(2)
Adding equations(1) and (2),we get
x^2+frac1x^2=161-72sqrt5+frac1161-72sqrt5
On rationalising the end term,we get
=161-72sqrt5+frac161+72sqrt5161^2-(72sqrt5)^2
=161-72sqrt5+frac161+72sqrt525921-25920
=161-72sqrt5+161+72sqrt5
=322
 

Posted by

Deependra Verma

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