Question

If $x^2+\frac{1}{x^2}=38$ , then what is the value of $\left| {x - \frac{1}{x}} \right|$

• A. 9
• B. 6
• C. 5
• D. 4

Answer 1

Answer:

B. 6

Given:

x² + $\frac{1}{x^2}$ = 38

Formula:

$(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-2$

| x | = x

| -x | = x

Calculation:

According to the formula

$(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-2$

⇒ $(x-\frac{1}{x})^2=38-2$

⇒ $(x-\frac{1}{x})=\sqrt{36}$

⇒ $(x-\frac{1}{x})=6$

Now,

$\left| {x - \frac{1}{x}} \right|$ =  | 6 | = 6.

Shortcut Trick

$x^2 + \frac{1}{x^2}=a$ then, $x-\frac{1}{x}=\sqrt{a}-2$

so if $x^2+\frac{1}{x^2}=38$ then $x-\frac{1}{x}=\sqrt{38-2}=\sqrt{36}=6$

$\left| {x - \frac{1}{x}} \right|$ =| 6 | = 6