[tex] |x - \frac{1}{x} | = 18 \\ [/tex]
So :
[tex]x - \frac{1}{x} = 18 \: \: \: or \: \: \: x - \frac{1}{x} = - 18 \\ [/tex]
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If
[tex]x - \frac{1}{x} = 18 \\ [/tex]
Multiply both sides by x
[tex]x \times (x - \frac{1}{x} ) = x \times 18 \\ [/tex]
[tex] {x}^{2} - 1 = 18x[/tex]
Subtract both sides 18x
[tex] {x}^{2} - 1 - 18x = 18x - 18x[/tex]
[tex] {x}^{2} - 18x - 1 = 0[/tex]
Thus the possible values for x from this equation are :
[tex]x = 9 + \sqrt{82} [/tex]
And
[tex]x = 9 - \sqrt{82} [/tex]
_____________________________________________
If
[tex]x - \frac{1}{x} = - 18 \\ [/tex]
Multiply both sides by x
[tex]x \times (x - \frac{1}{x} ) = x \times - 18 \\ [/tex]
[tex] {x}^{2} - 1 = - 18x[/tex]
Add both sides 18x
[tex] {x}^{2} - 1 + 18x = - 18x + 18x[/tex]
[tex] {x}^{2} + 18x - 1 = 0[/tex]
And the possible values for x from the above equation are :
[tex]x = - 9 + \sqrt{82} [/tex]
And
[tex]x = - 9 - \sqrt{82} [/tex]
_____________________________________________
Finally the possible answers would be :
[tex]x = 9 + \sqrt{82} [/tex]
[tex]x = 9 - \sqrt{82} [/tex]
[tex]x = - 9 + \sqrt{82} [/tex]
[tex]x = - 9 - \sqrt{82} [/tex]
There you go...
Have a great day ❤
