Question

if
$x + \frac{1}{x} = \frac{50}{7}$
then
$x - \frac{1}{x} =$

Answer 1

x+1/x = 50/7
Squaring on both sides....
x^2 +2 + 1/x^2 = 2500/49
Subtracting 4 on both sides...
x^2 -2 + 1/x^2 = (2500-196)/49
(x-1/x)^2 = 2304/49
x-1/x = 48/7

Answer 2

Solution :

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Given :

$x + \frac{1}{x} = \frac{50}{7}$

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To Find :

The value of
$x - \frac{1}{x}$,.

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The given data can also be written as,.

⇒ $x + \frac{1}{x} = \frac{50}{7}$

⇒ $\frac{x^2 + 1}{x} = \frac{50}{7}$

By cross-multiplication, we get,.

⇒ (x² + 1) 7 = 50 (x)

⇒ 7x² +7 = 50x

⇒ 7x² - 50x + 7 = 0,.

⇒ 7x² - 49x - x + 7 = 0

⇒ 7x (x - 7) + 1(x - 7) = 0

⇒ (7x - 1)(x - 7) = 0,.

For the equation to be zero,.

7x - 1 = 0,. (or) x - 7 = 0

Then,

we can say that,

⇒ 7x =  1 (or) x = 7

⇒ x = $\frac{1}{7}$ (or) x = 7

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Hence,.

x = 7 (or) x = $\frac{1}{7}$

⇒ x - $\frac{1}{x}$

if x = 7,.

Then,

⇒ $\frac{1}{x}$ = $\frac{1}{7}$ (or vice-versa),.

Hence,.

⇒ x - $\frac{1}{x}$

⇒ 7 -$( \frac{1}{7})$

⇒ $\frac{49 - 1}{7}$

⇒ $\frac{48}{7}$ = $6 \frac{6}{7}$

⇒ ∴ $x - \frac{1}{x} = 6 \frac{6}{7}$

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