If x+1/x=9 and x'+1/x'=53, Find the value of x-1/x
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If (x +1/x) = 9 and (x^2 + 1/x^2) = 53 then find the value of (x - 1/x)?
Given x+1/x=9 and x^2+1/x^2=53
x+1/x=9=>(x+1/x)^2=81=>x^2+1/x2+2=81=>x^2+1/x^2=79.
However if we assume x-1/x=A then
(x+1/x)(x-1/x)=9A=>x^2–1/x^2=9A and x^2+1/x2=53=>(53+9A)/2=2/(53–9A)
(53)^2-(2)^2=81A^2=>81A^2=55*51
A=(1/9)√(2805)
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