Question

if x is an intiger such that x+1/x=17/4 then the value of x-1/x is

Answer 1

I think you might satisfy from my answer

Answer 2

x+1/x =17/4

Square on both sides,

(x+1/x)²=(17/4)²

x²+1/x² +2= (289/16)

x²+1/x² =289/16 -2

x² +1/x² = (289-32)/16

x² +1/x² =257/16

Now,

Subtract 2(x*1/x) from both sides,

x²+1/x² -2 =(257/16) -2
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By formula (a-b)²=a²+b² -2ab
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(x-1/x)² =(257-32)/16

(x-1/x)² = 225/16

(x-1/x)² =(15/4)²

x-1/x =15/4

I hope this will help you

-by ABHAY