if x=√5+2 then x-1/x is
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x=√5+2
put the value of x in polynomial x-1/x
√5+2 - 1/√5+2
factorize the denominator for use the identity (a +b)(a - b) = a² - b²
√5+2 - 1/√5+2 × √5 - 2/√5 - 2
√5+2 - √5 - 2/(√5+2)(√5 - 2)
√5+2 - √5 - 2/(√5)² - 2²
√5+2 - √5 - 2/ 5 -4
√5+2 - √5 - 2/1
√5+2 - √5 - 2
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