Question

If x - 1/x = 6, find the value of x²+ 1/x².​

Answer 1

Step-by-step explanation:

Given , x+1x=6

Taking squares on both the sides , we get

(x+1x)2=62

⇒x2+1x2+2=36

⇒x2+1x2=34

Answer 2

Given:

$x - \frac{1}{x} = 6$

To find:

$The \: value \: of \: {x}^{2} + \frac{1}{ {x}^{2} }$

Solution:

To answer this question, we should know about one of the algebraic identities which is

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

Now,

As given, we have

$x - \frac{1}{x} = 6 \: (i)$

Squaring on both sides, we get

${(x - \frac{1}{x} )}^{2} = 36$

Now, using the above algebraic identity, we have,

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

So,

$36 = {x}^{2} + \frac{1}{ {x}^{2} } - 2$

[from (i)]

$36 + 2 = {x}^{2} + \frac{1}{ {x}^{2} }$

${x}^{2} + \frac{1}{ {x}^{2} } = 38$

Hence, the value of x²+ 1/x² is 38.