if x=√5+2,then find the value of x²+1/x² .
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Ans:- Given
x = √5+2
To find x²+1/x²
Solution:-
=> 1/x = 1/(√5+2)
=> 1/x = 1/(√5+2)×(√5-2)/(√5-2)
=> 1/x = (√5-2)/5-4
=> 1/x = √5-2
Now,
=> (x+1/x)² = x²+1/x²+2×x×1/x
=> (√5+2+√5-2)² = x²+1/x²+2
=> 5 = x²+1/x²+2
=> x²+1/x² = 3
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