Question

if X=1/x-5 find: x-1/x
and x+1/x​

Answer 1

Answer:

x=1/(x-5)

Or x-5=1/x since x is not equal to zero

Or x-1/x=5 ………(1)

Squaring both sides

(x-1/x)^2=25

Or x^2–2×x×(1/x)+1/(x^2)=25

Or x^2–2+1/(x^2)=25

Or x^2+1/(x^2)=25+2=27

Adding 2 to both sides we have

x^2+2+1/(x^2)=29

Or x^2+2×x×(1/x)+1/(x^2)=29

Or (x+1/x)^2=29

Or x+1/x=+-(29)^(1/2)………(2)

Multiplying (1) and (2) we have

x^2–1/x^2=+-5×(29)^(1/2)