Question

If x2+1/x2= 38..then find the value of x-1/x

Answer 1

The value of $x-\dfrac{1}{x}$ is $\pm 6$.

Tips:

Before we solve the problem, let us know some algebraic identities:

• $a^{2}+b^{2}=(a-b)^{2}+2ab$
• $a^{2}+b^{2}=(a+b)^{2}-2ab$
• $a^{2}-b^{2}=(a+b)(a-b)$

Step-by-step explanation:

Given, $x^{2}+\dfrac{1}{x^{2}}=38$

$\Rightarrow (x)^{2}+(\dfrac{1}{x})^{2}=38$

$\Rightarrow (x-\dfrac{1}{x})^{2}+2\times x\times\dfrac{1}{x}=38$

• Hint. Used the formula $a^{2}+b^{2}=(a-b)^{2}+2ab$

$\Rightarrow (x-\dfrac{1}{x})^{2}+2=38$

$\Rightarrow (x-\dfrac{1}{x})^{2}=38-2=36$

• Hint. Transposing $2$ to the right hand side

$\Rightarrow (x-\dfrac{1}{x})^{2}=6^{2}$

$\Rightarrow \boxed{x-\dfrac{1}{x}=\pm 6}$

• Hint. Taking square root of both sides