Question

$x - 1 \div x = 9. find the value of {x}^{2} + 1 \div {x}^{2}$


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Answer 1

Answer:

Given x+1/x=9 and x^2+1/x^2=53 this is not possible because

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).